21. From Mareg@csv.warwick.ac.uk (Dr DF Holt) Newsgroups Sci.math graham higman showed (Proc London Math Soc 10 (1960) 2430) that the numberb_n = log_p (a_n) / n^3 satisfies 2/27 - o(n) = b_n = 2/15 + o(n) where http://www.math.niu.edu/~rusin/known-math/97/numgrps

From: mareg@csv.warwick.ac.uk (Dr D F Holt) Newsgroups: sci.math Subject: Re: Groups and my software Date: 17 Oct 1997 09:56:13 +0100 In article , rusin@vesuvius.math.niu.edu (Dave Rusin) writes: > >Wilbert Dijkhof asked for a reference >for this result I had posted: > Let a_n be the number of non-isomorphic groups of order p^n. > Then log_p (a_n) is asymptotic to (2/27)n^3. > >Graham Higman showed (Proc London Math Soc 10 (1960) 24-30) that >the number b_n = log_p (a_n) / n^3 satisfies > 2/27 - o(n) <= 2/15 + o(n) >where the implied constant is independent of p. Later, Charles Sims >(Proc London Math Soc 15 (1965) 151-166) improved the upper bound to > b_n <= 2/27 + o(n) >(Again this is independent of p, although Higman's lower bound is >a little tighter than Sims' upper bound.) I am a little confused by your o(n) terms, since you have already divided through by n^3. More precisely, Higman proved n^3b_n >= 2n^3/27 + O(n^2) and Sims proved n^3b_n <= 2n^3/27 + O(n^(8/3)) > >Many more delicate results are also known for p-groups, partitioning the >set of those groups in various ways and then enumerating the parts. Counting >non-p-groups is rather more problematic, but good results have been obtained >by Laszlo Pyber (Ann Math 137 (1993) 203-220). Yes, Pyber showed that for any m>0, if f(m) denotes the number of isomorphism classes of groups of order m, and x is the highest exponent of any prime dividing m, then 2 (2/27 + o(1))x f(m)

22. Wales 1 Peter Brenda higman Pontypridd Glyntaff Cemetery 1 Done graham DouglasPorthcawl Cemetery 4 David Gregory Porthmadog 3 1/3 John Marshall Rhondda http://www.mapleleaflegacy.ca/mllpoct2000website/wales.html

Locations of Canadian War Graves in WALES Total: 403 commemorations in 53 cemeteries The cut off dates of death for war graves is: WWI - 31st August 1921 WWII - 31st December 1947 Anything after these dates should be veterans graves and not photographed. Please check in with the project representative before heading out to do any photography. He will know which ones have been done so far and may save you a trip. Red locations are done. Blue locations are assigned South Wales Angle St. Mary Churchyard 4 2/4 Pavel Vancata Beaufort St. David Churchyard 1 Done Arthur Roper Caerphilly Penyrheol Cemetery 1 Done Arthur Roper Cardiff Cathays Cemetery 8 - Done Steve Douglas Cardiff Western Cemetery 3 - Done Steve Douglas Carew St. Mary New Churchyard 5 Pavel Vancata Killay St. Hilary of Poictiers Churchyard 4 Llanbedr Moriah Calvinistic Methodist Churchyard 1 - two locations with this name Llanelli Box Cemetery 1 Jude Kent LLangybi (1st) St. Cybi Churchyard 1 Done John Marshall Llanshamlet Bethel Welsh Congregational Chapelyard 1 LLanwonno St. Gwynno Churchyard 1

23. Canadian_War_Graves_in_the_United_Kingdom_Including_England,_Scotland,_Wales,_No 1 graham Matthews BIDEFORD PUBLIC CEMETERY 1 Peter Brenda higman BIGGAR graham Douglas) 1 POOLE (PARKSTONE) CEMETERY 1 Done Peter higman POOLE http://www.mapleleaflegacy.ca/mllpoct2000website/unitedkingdom.html

Locations of Canadian War Graves in United Kingdom Including England, Scotland, Wales, Northern Ireland, Isle of Man Channel Islands, Orkney Islands, Shetland Islands, Western Isles A group of Canadian patients and staff at a hospital in England during the Great War TOTAL 12,685 commemorations in 1,217 cemeteries or memorials The cut off dates of death for war graves is : WWI - 31st August 1921 WWII - 31st December 1947 Anything after these dates should be veterans graves and not photographed. Please check in with the project representative before heading out to do any photography. He will know which ones have been done so far and may save you a trip. Red locations are done. Blue locations are assigned and awaiting completion. Burgundy locations are partly done. ABBOTSHALL PARISH CHURCHYARD 2 ABERDEEN GROVE CEMETERY 2 Neil Cameron, Martin Briscoe ABERDEEN (ALLENVALE) CEMETERY 14 Sandra Ross + 2 NCU Neil Cameron ABERDEEN (NELLFIELD) CEMETERY 3 2/3 Martin Briscoe ABERDEEN (SPRINGBANK) CEMETERY 4 2/4 done Neil Cameron ABERDEEN (ST. PETER'S) CEMETERY 2 1/2 Martin Briscoe

24. Sierra Club Holiday Party - 16 DEC 2003 71.17 KB Sue higman PC160068.jpg PC160068.jpg 62.92 KB Sue higman/Catherinegraham PC160071.jpg PC160071.jpg 69.77 KB Sue higman/Catherine graham http://www.swt.org/hikesierra/holiday03/

Sierra Club Holiday Party and Hike Story Telling 16 DEC 2003 Click on Small Images to See Full Images PC160001.JPG 149.73 KB Gerald Manata PC160002.JPG 162.25 KB Group PC160003.JPG 74.46 KB Group PC160005.JPG 165.91 KB Group PC160006.JPG 159.33 KB Group PC160007.JPG 162.73 KB Group PC160008.jpg 78.63 KB Ada Babine/Tony Biegen PC160011.jpg 53.84 KB Jim Vanyo PC160012.jpg 50.36 KB Jim Vanyo PC160015.JPG 49.25 KB Ada Babine PC160017.jpg 64.06 KB Ed Easton PC160019.jpg 68.87 KB Ed Easton PC160023.jpg 64.99 KB Larry Badash PC160024.jpg 65.66 KB Larry Badash PC160026.JPG 83.78 KB Tony Biegen PC160028.jpg 67.96 KB Tomi Sollen PC160030.jpg 66.87 KB Tomi Sollen PC160035.jpg 69.24 KB Jim Higman PC160038.jpg 77.38 KB Jim Higman PC160043.JPG 61.79 KB Bob Sollen PC160044.jpg 80.86 KB Bob Sollen PC160046.jpg 66.79 KB Catherine Graham PC160053.jpg 68.34 KB Linda Phillips PC160056.jpg 66.19 KB Linda Phillips PC160058.jpg 78.25 KB Sue Higman/Catherine Graham PC160060.jpg 71.17 KB Sue Higman PC160068.jpg 62.92 KB Sue Higman/Catherine Graham PC160071.jpg 69.77 KB Sue Higman/Catherine Graham Robert's Sierra Club Hikes Page Robert's Other Hikes Page Robert Bernstein Home Page

25. Search Results For Graham, Katharine - Encyclopædia Britannica graham higman University of St.Andrews, Scotland Brief introduction to the lifeand works of this English mathematician known for his research contributions http://www.britannica.com/search?query=graham, katharine&ct=

26. Royal Society | About The Society | About Us | The Fellowship | Directory Of Fel higman, Professor graham FRS. Elected , 1958. Medal(s) , Sylvester (1979).Email a friend Printer friendly. Select area http://www.royalsoc.ac.uk/view_fellow.cfm?FID=667

27. Royal Society | About The Society | Awards, Medals And Prize Lectures | | Sylves 1979 graham higman, for his distinguished and profoundly influential contributionsto the theory of finite and infinite groups. 1976 David George Kendall, http://www.royalsoc.ac.uk/page.asp?id=1766

28. Australian Mathematics Trust she stayed on at Oxford to do a D. Phil. under the supervision of graham higman . maiden name and Martin Powell was also a student of graham higman; http://www.amt.canberra.edu.au/bhnwilliamss.html

BH Neumann Award for Sheila Williams On Friday 12 April 2002, Professor BH Neumann presented a BH Neumann Award to Dr Sheila Williams. Sheila Williams receives her Award from Professor Neumann, at the function at Quay West Hotel, Brisbane. Sheila Williams with Neil (also a holder of this award) and Neil's parents Colin and Marjory. Citation Sheila Williams was born in Cornwall. Her parents were both teachers. Her father was in fact a school headmaster at Tintagel, on the north coast of Cornwall (where King Arthur is is said to have been born). She passed the notorious 11+ exam when she was ten, and went to Sir James Smith's Grammar School, Camelford. This was a very small school; less than 200 students and about 10 teachers. However, as is the case with so many of us, Sheila had an inspiring teacher, a Mr Alfred Hooper. He was a local, who, having got a first in mathematics at university, had chosen to go back to Cornwall to teach and those with any mathematical talent blossomed under his tutelage. When Sheila entered the sixth form she chose for her A level subjects Mathematics, Further Mathematics, Physics and Chemistry. She spent an extra year at school in order to take the Oxford Entrance examination, and was fortunate enough to win a scholarship to St Hugh's College, Oxford.

29. MANIFOLD-10: Authors They are both reseaching under the supervision of graham higman at Oxford.Chris is attached to Christchurch College, next to the famous meadow. http://www.jaworski.co.uk/m10/10_authors.html

manifold-10 manifold home page manifold 10 contents next article in manifold 10 ] [manifold 11 contents] These navigation links are repeated for convenience at the end of the article. authors R.L.Goodstein is professor of pure mathematics at the University of Leicester. He has written a number of articles popularising mathematics, including a number of essays on the philosophy of mathematics, his main research interest, in the Mathematical Gazette. H. Halberstam is professor of pure mathematics at Nottingham University. His main research interest is in elementary and analytic number theory, and part icularly in sieve methods. He and K. Roth wrote a book on Sequences. At present he is writing a book with H. E. Richert. R. Hart is a lecturer at Leeds University. The mathematics department there is most renowned for its ring theory group under Professor Goldie. Dr. Hart's main interest is in Noetherian rings. Douglas Woodall is a research fel-low in combinatorics at Nottingham. He has written a number of articles for Eureka. He sings in a choir and enjoys walking - he 'did' the Penine way last summer.

30. L. Scott - Collaborations An especially elementary proof, using observations by D. higman on work of Schur, group ring isomorphism problem (graham higman, Oxford thesis, 1940). http://www.math.virginia.edu/~lls2l/collaborations.htm

Although more than 20 items in Scott's bibliography are singly-authored, he often has preferred to work in collaboration. His principal collaborators are listed alphabetically below, followed by synopses of the collaborations, indexed to his bibliography. Michael Aschbacher, Professor of Mathematics, California Institute of Technology (NAS) George Avrunin, Professor of Mathematics, University of Massachusetts Edward Cline, Professor of Mathematics, University of Oklahoma Charles Curtis, Professor Emeritus, University of Oregon Jie Du, Senior Lecturer in Mathematics, University of New South Wales, Sydney Vlastimil Dlab, Distinguished Professor Emeritus, Carleton University, Ottawa (FRSC) Charles Dunkl, Professor of Mathematics, The University of Virginia Walter Feit, Professor Emeritus (deceased), Yale University (NAS) Wilburd van der Kallen, Department of Mathematics, University of Utrecht David Goldschmidt, Director of the Center for Communications Research, Princeton, formerly Professor of Mathematics, University of California at Berkeley Peter Hoefsmit, Industrial mathematician, Airborne Express Company

31. My Netscape FAQ Its isomorphism with the group of the same order found by graham higman at aroundthe same time will be demonstrated. We conclude with a brief overview of http://www.math.clemson.edu/~sgao/WEB/ADMSeminar/admf00.html

Fall 2000 Time: Thursday 3:30pm Room: Martin Hall M201 Aug 30 None Sept 7 Robert T. Curtis University of Birmingham, U.K. Symmetric generation of finite groups I Sept 14 Robert T. Curtis University of Birmingham, U.K. Symmetric generation of finite groups II Sept 21 Kevin James Clemson University Nonvanishing theorems for elliptic curves Sept 28 Kevin James Clemson University Continued Oct 5 Anant Godbole East Tennessee State University Oct 12 David Penniston Furman University Modular K3 surfaces Oct 19 Clemson Mini-Conference on Discrete Math. Oct 26 Neil J. Calkin Clemson University Counting sum-free and other sets of integers Nov 2 Morwen Thistlethwaite University of Tennessee Some applications of hyperbolic geometry in knot theory Nov 9 None Nov 16 Kelle Clark University of Virginia Bounds for the minumum weight of the dual codes of some classes of designs Nov 23 Thanksgiving Nov 30 George Fix Clemson University Minimal Homogeneous Bases for Ideals Dec 7 Robert T. Curtis University of Birmingham, U.K. Mathematics and the Art of M.C. Escher TITLE: Symmetric generation of finite groups I, II

32. Alan J. Cain -- Welcome To My Personal Homepage. EH Moore (18621932). Oswald Veblen (1880-1960). JHC Whitehead (1904-1960) ?graham higman, Stewart E. Stonehewer. John M. Howie, Edmund F. Robertson http://www.cenius.net/cain/maths/ancestry.php

Alan J. Cain Home C.V. Research Publications ... Links Address School of Mathematics and Statistics University of St Andrews North Haugh St Andrews Fife United Kingdom Office Email address Telephone I am a research fellow in the School of Mathematics and Statistics at the University of St Andrews I submitted my Ph.D. thesis, entitled Presentations for Subsemigroups of Groups and supervised by and Edmund Robertson , in July 2005. I have not yet had my viva. In July 2002 I graduated from the University of Glasgow , having obtained an M.Sci. in Mathematics with first-class honours. I was fortunate enough to be awarded a Carnegie Scholarship to fund my Ph.D. studies in St Andrews.

33. Electronic Research Announcements Macmillan, New York, 1964. MR 295889; 7. graham higman, ``Enumerating $p$ groups.I Inequalities , Proc. London Math. Soc. $(3)$ 10 (1960), 24-30. http://www.ams.org/era/2001-07-01/S1079-6762-01-00087-7/home.html

Journals Home Search Author Info Subscribe ... Help ISSN 1079-6762 Previous volume Table of contents Next volume Most recent volume ... All volumes The groups of order at most 2000 Author(s): Hans Ulrich Besche; Bettina Eick; E. A. O'Brien Journal: Electron. Res. Announc. Amer. Math. Soc. MSC (2000): Primary 20D10, 20D15; Secondary 20-04 Posted: February 12, 2001 Retrieve article in: PDF DVI TeX PostScript ... Additional information Abstract: We announce the construction up to isomorphism of the groups of order at most 2000. References: Hans Ulrich Besche, Bettina Eick, and E. A. O'Brien, ``A millennium project: constructing small groups'', Preprint. Hans Ulrich Besche and Bettina Eick, ``Construction of finite groups'', J. Symbolic Comput. MR Hans Ulrich Besche and Bettina Eick, ``The groups of order Comm. Algebra

34. Brent Everitt's Research A long standing conjecture (attributed to graham higman) asserts that each ofthe (p,q,r) triangle groups for 1/p+1/q+1/r 1 contains among its homomorphic http://www-users.york.ac.uk/~bje1/research.html

Research York Algebra group See also Papers (original article) The smallest hyperbolic 6-manifolds (with John Ratcliffe and Steve Tschantz) By gluing together copies of an all-right angled Coxeter polytope a number of open hyperbolic 6-manifolds with Euler characteristic -1 are constructed. They are the first known examples of hyperbolic 6-manifolds having the smallest possible volume. Electronic Research Announcements of the AMS (original article) Coxeter groups and hyperbolic manifolds (21 pages) The rich theory of Coxeter groups is used to provide an algebraic construction of finite volume hyperbolic n-manifolds. Combinatorial properties of finite images of these groups can be used to compute the volumes of the resulting manifolds. Three examples, in 4,5 and 6-dimensions, are given, each of very small volume, and in one case of smallest possible volume. Math. Annalen (original article) 3-Manifolds from Platonic Solids (8 pages) The problem of classifying the orientable spherical, Euclidean and hyperbolic 3-manifolds that arise by identifying the faces of a regular solid is phrased in the language of Coxeter groups. This allows us to complete the classification begun in the compact case by Richardson, Rubinstein and Lorimer. Topology and its Applications The Geometry and Topology of Groups (60 pages).

35. INDEX OF NAMES higman, graham (England, 1917 ) and axioms for groups, 1153 Hilbert, David (Germany,1862-1943) and axioms for geometry, 1154 and character of math, 1176 http://www.wolframscience.com/nksonline/index/names/f-j.html?SearchIndex=Hilbert

36. Walter Feit. In Memoriam His paper with graham higman became a fundamental building block and stimulateda large body of research on combinatorial structures. http://www.math.yale.edu/public_html/WalterFeit/Obit/FirstPage.html

Obituary In Memoriam: Mathematician Walter Feit, Pioneer in Finite Group Theory New Haven, Conn. - Mathematician Walter Feit, a Yale professor for 40 years, died at age 73 after a long illness on July 29, 2004 at the Connecticut Hospice in Branford, CT. Professor Feit was a pure mathematician whose contributions provided fundamental infrastructure used in algebra, geometry, topology, number theory, and logic. His work aided the development of practical applications in areas including cryptography, chemistry, and physics. Professor Feit's 1963 paper with John G. Thompson, "Solvability of Groups of Odd Order," filled an entire issue of the Pacific Journal of Mathematics and is widely regarded as the most influential paper ever written on finite group theory. It energized the field, providing both inspiration and technical tools for the research that finally culminated in the complete classification of simple finite groups. Finite group theory was only one of several areas invigorated by Professor Feit's insights. His paper with Graham Higman became a fundamental building block and stimulated a large body of research on combinatorial structures. His work on Schur indices revitalized progress in that subject as well. Feit joined the Yale faculty of mathematics in 1964. He served the Yale mathematics department in several administrative roles, acting as Director of Undergraduate Studies, Director of Graduate Studies, and Chairman. His standing in the mathematics community was marked by award of the American Mathematical Society Cole Prize in Algebra, election to the National Academy of Sciences and the American Academy of Arts and Sciences, editorship of various journals, and Vice-Presidency of the International Mathematical Union.

37. Martyn Quick: Mathematical Genealogy Summary MRQuick MRVaughan-Lee - PMNeumann - G.higman - JHCWhitehead - O.Veblen -EHMoore D.Phil. University of Oxford 1966 Advisor graham higman http://www-groups.mcs.st-andrews.ac.uk/~martyn/collaborations/genealogy.html

General Information Collaborations News ... Martyn Quick Mathematical Genealogy The following information has been retrieved from the Mathematics Genealogy Project . The biography links are to those stored in the MacTutor History of Mathematics archive at the School of Mathematics and Statistics in St. Andrews. Summary: M.R.Quick M.R.Vaughan-Lee P.M.Neumann G.Higman ... G.W.Leibniz Martyn R. Quick D.Phil. University of Oxford 1995 Dissertation: Varieties of Groups of Exponent Four Advisor: Michael Vaughan-Lee Michael R. Vaughan-Lee Homepage D.Phil. University of Oxford 1968 Advisor: Peter Neumann Peter M. Neumann Homepage D.Phil. University of Oxford 1966 Advisor: Graham Higman Graham Higman D.Phil. University of Oxford 1941 Dissertation: The Units of Group-Rings Advisor: John Whitehead John Henry Constantine Whitehead Ph.D. Princeton University 1930 Dissertation: The Representation of Projective Spaces Advisor: Oswald Veblen Oswald Veblen Ph.D. University of Chicago 1903 Dissertation: A System of Axioms for Geometry Advisor: E.H. Moore

38. Jakob Nielsen Papers higman, graham 7 reprints. Hilb, Emil 1 reprint. Hilbert, David 3 reprints.Hoff, Ove 2 reprints. Holm, AR 1 reprint. Holmberg, Erik 1 reprint. http://www.math.ku.dk/arkivet/jnielsen/jnpapers.htm

THE ARCHIVE INSTITUTE FOR MATHEMATICAL SCIENCES THE UNIVERSITY OF COPENHAGEN The homepage of the archive List of collections Jakob Nielsen papers General, short description of the collection A short biography of Nielsen A survey of the content People from whom there is more than reprints ... Details about the content of some of the folders General, short description of the collection A short description: This collection of Jakob Nielsen papers consists mainly of reprints, which Nielsen has received from other scientists and sorted by authors. In addition to the reprints there is other material from some of the persons, i.e. letters, manuscripts, applications for positions etc. All the material is from the period around 1890-1959 and the reprints are in many different languages. However, the additional material is mainly in Danish or German. Size: The collection is contained in 79 archival boxes of which the first 25 are standard boxes while the rest are Nielsen's original boxes. Handed over: The collection was located in the basement of the mathematical library in the E block of the H. C. Ørsted Institute in the fall of 1996. It is not known when and how it was put here. Photocopies of material from the Staatsarchiv Hamburg was added to box 10 in July 1999.

39. Jakob Nielsen Papirer higman, graham 7 særtryk. Hilb, Emil 1 særtryk. Hilbert, David 3 særtryk.Hoff, Ove 2 særtryk. Holm, AR 1 særtryk. Holmberg, Erik 1 særtryk. http://www.math.ku.dk/arkivet/jnielsen/jnarkiv.htm

ARKIVET INSTITUT FOR MATEMATISKE FAG KØBENHAVNS UNIVERSITET Arkivets hjemmeside Samlingsoversigt Jakob Nielsen papirer Overordnet beskrivelse af samlingen Kort biografi Oversigt over indholdet Personer, hvorfra der er andet end særtryk ... Detaljeret om indholdet i enkelte mapper Overordnet beskrivelse af samlingen Kort beskrivelse: Denne samling af Jakob Nielsens papirer består for størstedelen af særtryk, som Nielsen har modtaget fra andre videnskabsfolk og sorteret efter forfatter. Udover særtrykkene er der i forbindelse med nogle af personerne breve, manuskripter, ansøgninger og andet. Alt materiale er fra ca. 1890-1959 og på en lang række sprog hvad angår særtrykkene. Det øvrige materiale er dog fortrinsvis på dansk eller tysk. Omfang: Samlingen omfatter 79 arkivkasser, hvoraf de første 25 er almindelige arkivkasser og resten er Nielsens originale kasser. Overdragelse: Samlingen befandt sig i Matematisk biblioteks kælder i E-bygningen på H. C. Ørsted Institutet i efteråret 1996. Det vides ikke, hvornår eller hvordan den er kommet der. I juli 1999 blev der tilføjet fotokopier af materiale fra Staatsarchiv Hamburg til box 10 Klausuler: Ingen.

40. Graph Theorist Families Translate this page EH Moore, Oswald Veblen, John HC Whitehead, graham higman, Peter M. Neumann,Peter J. Cameron. EH Moore, Oswald Veblen, John HC Whitehead, graham higman http://www.cs.columbia.edu/~sanders/graphtheory/people/families.html

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