[PDF] The Spread Of Almost Simple Classical Groups eBook

Author : Scott Harper
Publisher : Springer Nature
Page : 154 pages
File Size : 37,12 MB
Release : 2021-05-25
Category : Mathematics
ISBN : 3030741001

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This monograph studies generating sets of almost simple classical groups, by bounding the spread of these groups. Guralnick and Kantor resolved a 1962 question of Steinberg by proving that in a finite simple group, every nontrivial element belongs to a generating pair. Groups with this property are said to be 3/2-generated. Breuer, Guralnick and Kantor conjectured that a finite group is 3/2-generated if and only if every proper quotient is cyclic. We prove a strong version of this conjecture for almost simple classical groups, by bounding the spread of these groups. This involves analysing the automorphisms, fixed point ratios and subgroup structure of almost simple classical groups, so the first half of this monograph is dedicated to these general topics. In particular, we give a general exposition of Shintani descent. This monograph will interest researchers in group generation, but the opening chapters also serve as a general introduction to the almost simple classical groups.

Author : Timothy C. Burness
Publisher : Cambridge University Press
Page : 365 pages
File Size : 26,16 MB
Release : 2016-01-15
Category : Mathematics
ISBN : 1107629446

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A graduate-level introduction to finite classical groups featuring a comprehensive account of the conjugacy and geometry of elements of prime order.

Author : C. M. Campbell
Publisher : Cambridge University Press
Page : 510 pages
File Size : 12,59 MB
Release : 2019-04-11
Category : Mathematics
ISBN : 110872874X

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These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.

Author : Konrad K. Dabrowski
Publisher : Cambridge University Press
Page : 380 pages
File Size : 48,74 MB
Release : 2021-06-24
Category : Mathematics
ISBN : 1009041819

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This volume contains nine survey articles based on plenary lectures given at the 28th British Combinatorial Conference, hosted online by Durham University in July 2021. This biennial conference is a well-established international event, attracting speakers from around the world. Written by some of the foremost researchers in the field, these surveys provide up-to-date overviews of several areas of contemporary interest in combinatorics. Topics discussed include maximal subgroups of finite simple groups, Hasse–Weil type theorems and relevant classes of polynomial functions, the partition complex, the graph isomorphism problem, and Borel combinatorics. Representing a snapshot of current developments in combinatorics, this book will be of interest to researchers and graduate students in mathematics and theoretical computer science.

Author : Bridget S. Webb
Publisher : Cambridge University Press
Page : 270 pages
File Size : 31,34 MB
Release : 2005-07-21
Category : Mathematics
ISBN : 9780521615235

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This volume provides an up-to-date overview of current research across combinatorics,.

Author : C. M. Campbell
Publisher : Cambridge University Press
Page : 503 pages
File Size : 38,50 MB
Release : 2015-10-22
Category : Mathematics
ISBN : 1316467910

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Every four years, leading researchers gather to survey the latest developments in all aspects of group theory. Since 1981, the proceedings of those meetings have provided a regular snapshot of the state of the art in group theory and helped to shape the direction of research in the field. This volume contains selected papers from the 2013 meeting held in St Andrews. It begins with major articles from each of the four main speakers: Emmanuel Breuillard (Paris-Sud), Martin Liebeck (Imperial College London), Alan Reid (Texas) and Karen Vogtmann (Cornell). These are followed by, in alphabetical order, survey articles contributed by other conference participants, which cover a wide spectrum of modern group theory.