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The spread of almost simple classica...

Harper, Scott.

The spread of almost simple classical groups

Record Type:	Electronic resources : Monograph/item
Title/Author:	The spread of almost simple classical groupsby Scott Harper.
Author:	Harper, Scott.
Published:	Cham :Springer International Publishing :2021.
Description:	viii, 154 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Group theory.
Online resource:	https://doi.org/10.1007/978-3-030-74100-6
ISBN:	9783030741006$q(electronic bk.)

The spread of almost simple classical groups
Harper, Scott.

The spread of almost simple classical groups[electronic resource] /by Scott Harper. - Cham :Springer International Publishing :2021. - viii, 154 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v.22860075-8434 ;. - Lecture notes in mathematics ;2035..

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.

ISBN: 9783030741006$q(electronic bk.)

Standard No.: 10.1007/978-3-030-74100-6doiSubjects--Topical Terms:

189579
Group theory.

LC Class. No.: QA174.2 / .H37 2021

Dewey Class. No.: 512.2

The spread of almost simple classical groups
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520 $a 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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