arXiv Analytics

Sign in

arXiv:1903.00748 [math.GR]AbstractReferencesReviewsResources

Girth, words and diameter

Martin W. Liebeck, Aner Shalev

Published 2019-03-02Version 1

We study the girth of Cayley graphs of finite classical groups G on random sets of generators. Our main tool is an essentially best possible bound we obtain on the probability that a given word w takes the value 1 when evaluated in G in terms of the length of w, which has additional applications. We also study the girth of random directed Cayley graphs of symmetric groups, and the relation between the girth and the diameter of random Cayley graphs of finite simple groups.

Comments: To appear in Bull. London Math. Soc
Categories: math.GR, math.CO, math.PR
Subjects: 20D06, 20P05, 05C80, 05C12
Related articles: Most relevant | Search more
arXiv:1910.03623 [math.GR] (Published 2019-10-08)
Invariable generation of finite classical groups
arXiv:1409.8086 [math.GR] (Published 2014-09-29)
On the structure of finite groups isospectral to finite simple groups
arXiv:1312.4998 [math.GR] (Published 2013-12-17)
A Refined Waring Problem for Finite Simple Groups

Links

Toolbox