English

Connectivity of the Product Replacement Algorithm Graph of PSL(2,q)

Group Theory 2010-03-17 v2

Abstract

The product replacement algorithm is a practical algorithm to construct random elements of a finite group G. It can be described as a random walk on a graph whose vertices are the generating k-tuples of G (for a fixed k). We show that if G is PSL(2,q) or PGL(2,q), where q is a prime power, then this graph is connected for any k>=4. This generalizes former results obtained by Gilman and Evans.

Keywords

Cite

@article{arxiv.0712.1357,
  title  = {Connectivity of the Product Replacement Algorithm Graph of PSL(2,q)},
  author = {Shelly Garion},
  journal= {arXiv preprint arXiv:0712.1357},
  year   = {2010}
}

Comments

12 pages. This article was submitted to the Journal of Group Theory on July 2007 and accepted on December 2007

R2 v1 2026-06-21T09:52:09.935Z