Abstract
Given a finite group G, the Dirichlet polynomial of G is
The multiplicative counterpart of this polynomial is called the Probabilistic Zeta function of the group G. We prove that if H is a finite group such that P G (s) = P H (s), then G and H have the same non-Frattini abelian chief factors.
2010 Mathematics Subject Classification:
Notes
Communicated by P. Tiep.