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The Spread Of Almost Simple Classical Groups 1st Ed 2021 Scott Harper

  • SKU: BELL-51793220
The Spread Of Almost Simple Classical Groups 1st Ed 2021 Scott Harper
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The Spread Of Almost Simple Classical Groups 1st Ed 2021 Scott Harper instant download after payment.

Publisher: Springer
File Extension: PDF
File size: 2.37 MB
Pages: 164
Author: Scott Harper
ISBN: 9783030740993, 3030740994
Language: English
Year: 2021
Edition: 1st ed. 2021

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The Spread Of Almost Simple Classical Groups 1st Ed 2021 Scott Harper by Scott Harper 9783030740993, 3030740994 instant download after payment.


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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