Resumen de The probabilistic zeta function of PSL(2,q), of the Suzuki groups ² B2(q) and of the Ree groups ²G2(q)

Massimiliano Patassini

• We study the Dirichlet polynomial PG(s) of the groups G = PSL(2,q), 2 B2(q), and 2G2(q). For such G we show that if H is a group satisfying PH(s) = PG(s), then H / Frat(H)?G. We also prove that, when q is not a prime number, PG(s) is irreducible in the ring of Dirichlet polynomials. Finally, we prove that the coset poset of G is noncontractible.