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arXiv · 0712.1357

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

Shelly Garion
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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.

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Shelly Garion. 2007-12-30. Connectivity of the Product Replacement Algorithm Graph of PSL(2,q). https://doi.org/10.1515/jgt.2008.048

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