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

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

2007-12-09

arxiv.org/abs/0712.1357v2

J. Group Theory 11 (2008), 765-777

Mathematics

Group Theory

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

Scientific paper

10.1515/JGT.2008.048

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.

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