The spread of almost simple classical groups / Scott Harper.
2021
QA174.2
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Title
The spread of almost simple classical groups / Scott Harper.
ISBN
9783030741006 (electronic bk.)
3030741001 (electronic bk.)
9783030741013 (print)
303074101X
3030740994
9783030740993
3030741001 (electronic bk.)
9783030741013 (print)
303074101X
3030740994
9783030740993
Published
Cham, Switzerland : Springer, [2021]
Language
English
Description
1 online resource
Item Number
10.1007/978-3-030-74100-6 doi
Call Number
QA174.2
Dewey Decimal Classification
512/.2
Summary
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.
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Includes bibliographical references.
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Source of Description
Online resource; title from PDF title page (SpringerLink, viewed June 2, 2021).
Series
Lecture notes in mathematics (Springer-Verlag) ; 2286. 0075-8434
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Spread of almost simple classical groups.
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Table of Contents
Introduction
Preliminaries
Shintani Descent
Fixed Point Ratios
Orthogonal Groups
Unitary Groups.
Preliminaries
Shintani Descent
Fixed Point Ratios
Orthogonal Groups
Unitary Groups.