Let G be a finite group. There is a Dirichlet polynomial P(G,s) associated with G, with the property that for all t∈N, P(G,t) is the probability that t random elements of G generate G. We investigate connections between the factorization of P(G,s) in the ring of Dirichlet polynomials, and the structure of G. If P(G,s) is simple then G/FratG is simple. We investigate whether the converse is true, studying the factorization in the case of some finite simple groups.
Some properties of the probabilistic zeta function on finite simple groups
LUCCHINI, ANDREA;
2004
Abstract
Let G be a finite group. There is a Dirichlet polynomial P(G,s) associated with G, with the property that for all t∈N, P(G,t) is the probability that t random elements of G generate G. We investigate connections between the factorization of P(G,s) in the ring of Dirichlet polynomials, and the structure of G. If P(G,s) is simple then G/FratG is simple. We investigate whether the converse is true, studying the factorization in the case of some finite simple groups.File in questo prodotto:
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