The Spread Of Almost Simple Classical Groups

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The Spread Of Almost Simple Classical Groups

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Author : Scott Harper
language : en
Publisher: Springer Nature
Release Date : 2021-05-25

The Spread Of Almost Simple Classical Groups written by Scott Harper and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-25 with Mathematics categories.

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.

The Spread Of Almost Simple Classical Groups

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Author : Scott Harper
language : en
Publisher: Springer
Release Date : 2021-05-26

The Spread Of Almost Simple Classical Groups written by Scott Harper and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-26 with Mathematics categories.

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.

Classical Groups Derangements And Primes

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Author : Timothy C. Burness
language : en
Publisher: Cambridge University Press
Release Date : 2016-01-15

Classical Groups Derangements And Primes written by Timothy C. Burness and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-15 with Mathematics categories.

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

Groups St Andrews 2017 In Birmingham

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Author : C. M. Campbell
language : en
Publisher: Cambridge University Press
Release Date : 2019-04-11

Groups St Andrews 2017 In Birmingham written by C. M. Campbell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-11 with Mathematics categories.

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

Normal 2 Coverings Of The Finite Simple Groups And Their Generalizations

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Author : Daniela Bubboloni
language : en
Publisher: Springer Nature
Release Date : 2024-07-22

Normal 2 Coverings Of The Finite Simple Groups And Their Generalizations written by Daniela Bubboloni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-22 with Mathematics categories.

This book provides a complete and comprehensive classification of normal 2-coverings of non-abelian simple groups and their generalizations. While offering readers a thorough understanding of these structures, and of the groups admitting them, it delves into the properties of weak normal coverings. The focal point is the weak normal covering number of a group G, the minimum number of proper subgroups required for every element of G to have a conjugate within one of these subgroups, via an element of Aut(G). This number is shown to be at least 2 for every non-abelian simple group and the non-abelian simple groups for which this minimum value is attained are classified. The discussion then moves to almost simple groups, with some insights into their weak normal covering numbers. Applications span algebraic number theory, combinatorics, Galois theory, and beyond. Compiling existing material and synthesizing it into a cohesive framework, the book gives a complete overview of this fundamental aspect of finite group theory. It will serve as a valuable resource for researchers and graduate students working on non-abelian simple groups,

Surveys In Combinatorics 2005

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Author : Bridget S. Webb
language : en
Publisher: Cambridge University Press
Release Date : 2005

Surveys In Combinatorics 2005 written by Bridget S. Webb and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Combinatorial analysis categories.

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

Surveys In Combinatorics 2021

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Author : Konrad K. Dabrowski
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-24

Surveys In Combinatorics 2021 written by Konrad K. Dabrowski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-24 with Mathematics categories.

These nine articles provide up-to-date surveys of topics of contemporary interest in combinatorics.

Expansion In Finite Simple Groups Of Lie Type

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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-16

Expansion In Finite Simple Groups Of Lie Type written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-16 with Mathematics categories.

Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemerédi-Gowers lemma. Applications to the affine sieve of Bourgain, Gamburd, and Sarnak are also given. The material is largely self-contained, with additional sections on the general theory of expanders, spectral theory, Lie theory, and the Lang-Weil bound, as well as numerous exercises and other optional material.

Groups St Andrews 2013

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Author : C. M. Campbell
language : en
Publisher: Cambridge University Press
Release Date : 2015-10-22

Groups St Andrews 2013 written by C. M. Campbell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-22 with Mathematics categories.

Leading researchers survey the latest developments in group theory and many related areas.

Asymptotic Spreading For General Heterogeneous Fisher Kpp Type Equations

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Author : Henri Berestycki
language : en
Publisher: American Mathematical Society
Release Date : 2022-11-10

Asymptotic Spreading For General Heterogeneous Fisher Kpp Type Equations written by Henri Berestycki and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-10 with Mathematics categories.

View the abstract.