Let G be a finite group; there exists a uniquely determined Dirichlet polynomial P(G,s) such that if t is a positive integer, then P(G,t) gives the probability of generating G with t randomly chosen elements. We show that it may be recognized from the knowledge of P(G,s) whether G/Frat(G) iis a simple group.
The probabilistic zeta function of finite simple groups
LUCCHINI, ANDREA;
2007
Abstract
Let G be a finite group; there exists a uniquely determined Dirichlet polynomial P(G,s) such that if t is a positive integer, then P(G,t) gives the probability of generating G with t randomly chosen elements. We show that it may be recognized from the knowledge of P(G,s) whether G/Frat(G) iis a simple group.
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