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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
Links to Related Works	Subject References: Group theory . Group Theory and Generalizations . Authors: Harper, Scott . Series: Lecture notes in physics . Classification: 512.2 . 512.2 (DDC 23) .

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The Spread of Almost Simple Classical Groups

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