, Volume 134, Issue 2, pp 251-299

Walks on generating sets of groups

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Abstract.

We study a Markov chain on generating n-tuples of a fixed group which arises in algorithms for manipulating finite groups. The main tools are comparison of two Markov chains on different but related state spaces and combinatorics of random paths. The results involve group theoretical parameters such as the size of minimal generating sets, the number of distinct generating k-tuples for different k's and the maximal diameter of the group.

Oblatum 6-VIII-1996 & 6-XI-97