The depth of a finite simple group

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Title: The depth of a finite simple group
Authors: Burness, TC
Liebeck, MW
Shalev, A
Item Type: Journal Article
Abstract: We introduce the notion of the depth of a finite group G, defined as the minimal length of an unrefinable chain of subgroups from G to the trivial subgroup. In this paper we investigate the depth of (non-abelian) finite simple groups. We determine the simple groups of minimal depth, and show, somewhat surprisingly, that alternating groups have bounded depth. We also establish general upper bounds on the depth of simple groups of Lie type, and study the relation between the depth and the much studied notion of the length of simple groups. The proofs of our main theorems depend (among other tools) on a deep number-theoretic result, namely, Helfgott’s recent solution of the ternary Goldbach conjecture.
Issue Date: 16-Feb-2018
Date of Acceptance: 29-Aug-2017
URI: http://hdl.handle.net/10044/1/50545
DOI: https://dx.doi.org/10.1090/proc/13937
ISSN: 0002-9939
Publisher: American Mathematical Society
Start Page: 2343
End Page: 2358
Journal / Book Title: Proceedings of the American Mathematical Society
Volume: 146
Issue: 6
Copyright Statement: © Copyright 2018 American Mathematical Society
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
CHAIN DIFFERENCE ONE
LIE TYPE
MAXIMAL-SUBGROUPS
EXCEPTIONAL GROUPS
LENGTH
GENERATION
0101 Pure Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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