For a given finite group G there exists a uniquely determined Dirichlet polynomial P(G,s) with the property that for t is an element of N the number P(G,t) coincides with the probability of generating G by t randomly chosen elements. We discuss whether the isomorphism type of a simple group G can be determined by the knowledge of P(G,s).
On the Dirichlet polynomial of finite groups of Lie type
LUCCHINI, ANDREA;
2006
Abstract
For a given finite group G there exists a uniquely determined Dirichlet polynomial P(G,s) with the property that for t is an element of N the number P(G,t) coincides with the probability of generating G by t randomly chosen elements. We discuss whether the isomorphism type of a simple group G can be determined by the knowledge of P(G,s).
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