Rationality of the probabilistic zeta functions of finitely generated profinite groups

Duong Hoang Dung; Andrea Lucchini

doi:10.1515/jgt-2013-0037

Rationality of the probabilistic zeta functions of finitely generated profinite groups

Duong Hoang Dung, Andrea Lucchini

Laboratory of Mathematical Design for Advanced Cryptography

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We prove that if the probabilistic zeta function P_G(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 language	English
Pages (from-to)	317-335
Number of pages	19
Journal	Journal of Group Theory
Volume	17
Issue number	2
DOIs	https://doi.org/10.1515/jgt-2013-0037
Publication status	Published - Mar 1 2014

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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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.",

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Rationality of the probabilistic zeta functions of finitely generated profinite groups

Abstract

All Science Journal Classification (ASJC) codes

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