A finiteness condition on the coefficients of the probabilistic Zeta function

Duong Hoang Dung, Andrea Lucchini

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We discuss whether finiteness properties of a profinite group G can be deduced from the coeffcients of the probabilistic zeta function PG(s). In particular we prove that if PG(s) is rational and all but finitely many non abelian composition factors of G are isomorphic to PSL(2; p) for some prime p, then G contains only finitely many maximal subgroups.

Original languageEnglish
Pages (from-to)167-174
Number of pages8
JournalInternational Journal of Group Theory
Volume2
Issue number1
Publication statusPublished - Jan 1 2013

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Profinite Groups
Finiteness Conditions
Maximal Subgroup
Finiteness
Riemann zeta function
Isomorphic
Coefficient

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

A finiteness condition on the coefficients of the probabilistic Zeta function. / Dung, Duong Hoang; Lucchini, Andrea.

In: International Journal of Group Theory, Vol. 2, No. 1, 01.01.2013, p. 167-174.

Research output: Contribution to journalArticle

Dung, Duong Hoang ; Lucchini, Andrea. / A finiteness condition on the coefficients of the probabilistic Zeta function. In: International Journal of Group Theory. 2013 ; Vol. 2, No. 1. pp. 167-174.
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