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The Spread of Almost Simple Classical Groups
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Catalogue Information
Field name
Details
Dewey Class
512.2
Title
The Spread of Almost Simple Classical Groups ([EBook]) / Scott Harper
Author
Harper, Scott
Publication
Cham : Springer International Publishing , 2021
Physical Details
: online resource (viii, 154 p. ill.)
Series
Lecture notes in physics
; 2286
ISBN
978-3-030-74100-6
Summary Note
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.:
Mode of acces to digital resource
Digital reproduction.- Cham : Springer International Publishing, 2021. - Digital book. Cham Springer Nature 2021. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site
https://doi.org/10.1007/978-3-030-74100-6
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Subject References:
Group theory
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Group Theory and Generalizations
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Authors:
Harper, Scott
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Series:
Lecture notes in physics
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Classification:
512.2
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512.2 (DDC 23)
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