Imperial College London
Professor Martin Liebeck

ProfessorMartinLiebeck

Faculty of Natural Sciences, Department of Mathematics

Head of Pure Mathematics Section/Prof of Pure Mathematics
 
 
 
//

Contact

 

+44 (0)20 7594 8490m.liebeck Website

 
 
//

Location

 

665Huxley BuildingSouth Kensington Campus

//

Summary

 

Publications

Citation

BibTex format

@article{Burness:2018:proc/13937,
author = {Burness, TC and Liebeck, MW and Shalev, A},
doi = {proc/13937},
journal = {Proceedings of the American Mathematical Society},
pages = {2343--2358},
title = {The depth of a finite simple group},
url = {http://dx.doi.org/10.1090/proc/13937},
volume = {146},
year = {2018}
}
Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We introduce the notion of the depth of a finite group G, defined as theminimal length of an unrefinable chain of subgroups from G to the trivial subgroup. Inthis paper we investigate the depth of (non-abelian) finite simple groups. We determinethe simple groups of minimal depth, and show, somewhat surprisingly, that alternatinggroups have bounded depth. We also establish general upper bounds on the depth ofsimple groups of Lie type, and study the relation between the depth and the much studiednotion of the length of simple groups. The proofs of our main theorems depend (amongother tools) on a deep number-theoretic result, namely, Helfgott’s recent solution of theternary Goldbach conjecture.
AU  - Burness,TC
AU  - Liebeck,MW
AU  - Shalev,A
DO  - proc/13937
EP  - 2358
PY  - 2018///
SN  - 0002-9939
SP  - 2343
TI  - The depth of a finite simple group
T2  - Proceedings of the American Mathematical Society
UR  - http://dx.doi.org/10.1090/proc/13937
UR  - http://hdl.handle.net/10044/1/50545
VL  - 146
ER  -
Download