Girth, words and diameter
Group Theory
2019-03-25 v2 Combinatorics
Probability
Abstract
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.
Cite
@article{arxiv.1903.00748,
title = {Girth, words and diameter},
author = {Martin W. Liebeck and Aner Shalev},
journal= {arXiv preprint arXiv:1903.00748},
year = {2019}
}
Comments
To appear in Bull. London Math. Soc