TR-227: The Probability of Generating Some Common Families of Finite Groups

Carleton University
Technical Report TR-227
November 1993

The Probability of Generating Some Common Families of Finite Groups

Let G be a finite group. Define e( G) to be the expected number of elements of G which have to be drawn at random with replacement from G before a set of generators is found. Define An ( G) to be the pro babil­ity that n elements drawn at random with replacement from G generate G. In this paper we discuss some general approaches to computing e(G)
and An ( G). We apply these approaches to some common classes of finite groups, including the p-groups and the nilpotent groups.

TR-227.pdf

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