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The Spread of Almost Simple Classical Groups

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Spread of Almost Simple Classical Groups/ by Scott Harper.
作者:	Harper, Scott.
面頁冊數:	VIII, 154 p. 35 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Group Theory and Generalizations. -
電子資源:	https://doi.org/10.1007/978-3-030-74100-6
ISBN:	9783030741006

The Spread of Almost Simple Classical Groups
Harper, Scott.

The Spread of Almost Simple Classical Groups[electronic resource] /by Scott Harper. - 1st ed. 2021. - VIII, 154 p. 35 illus.online resource. - Lecture Notes in Mathematics,22861617-9692 ;. - Lecture Notes in Mathematics,2144.

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

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

672112
Group Theory and Generalizations.

LC Class. No.: QA174-183

Dewey Class. No.: 512.2

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