Rationality of the probabilistic zeta functions of finitely generated profinite groups

Dung Hoang Duong, Andrea Lucchini

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We prove that if the probabilistic zeta function PG(s) of a finitely generated profinite group G is rational and all but finitely many nonabelian composition factors of G are groups of Lie type in a fixed characteristic or sporadic simple groups, then G contains only finitely many maximal subgroups.

Original languageEnglish
Pages (from-to)317-335
Number of pages19
JournalJournal of Group Theory
Volume17
Issue number2
DOIs
Publication statusPublished - Mar 1 2014

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Sporadic Simple Groups
Groups of Lie Type
Profinite Groups
Maximal Subgroup
Finitely Generated Group
Rationality
Riemann zeta function

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Rationality of the probabilistic zeta functions of finitely generated profinite groups. / Duong, Dung Hoang; Lucchini, Andrea.

In: Journal of Group Theory, Vol. 17, No. 2, 01.03.2014, p. 317-335.

Research output: Contribution to journalArticle

Duong, Dung Hoang ; Lucchini, Andrea. / Rationality of the probabilistic zeta functions of finitely generated profinite groups. In: Journal of Group Theory. 2014 ; Vol. 17, No. 2. pp. 317-335.
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