We prove that a finite group G is p-soluble if and only if the Dirichlet polynomial P(G,s) is p-multiplicative. Moreover, we show that one can recover the et of prime divisors of the order of G from the knowledge of P(G,s).
Finite groups with p-multiplicative probabilistic zeta function
LUCCHINI, ANDREA
2007
Abstract
We prove that a finite group G is p-soluble if and only if the Dirichlet polynomial P(G,s) is p-multiplicative. Moreover, we show that one can recover the et of prime divisors of the order of G from the knowledge of P(G,s).
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