Let G be a finite group; there exists a uniquely determined Dirichlet polynomial P(G,s) such that if t is an element of N, then P(G,t) gives the probability of generating G with t randomly chosen elements. We show that if P(G,s) = P(Alt(n),s), then G/Frat G congruent to Alt(n).
Recognizing the alternating groups from their probabilistic zeta function
LUCCHINI, ANDREA
2004
Abstract
Let G be a finite group; there exists a uniquely determined Dirichlet polynomial P(G,s) such that if t is an element of N, then P(G,t) gives the probability of generating G with t randomly chosen elements. We show that if P(G,s) = P(Alt(n),s), then G/Frat G congruent to Alt(n).
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