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

• Autores: Massimiliano Patassini
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 240, Nº 1, 2009, págs. 185-200
• Idioma: inglés
• DOI: 10.2140/pjm.2009.240.185
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.