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Rationality of the probabilistic zeta functions of finitely generated profinite groups

Journal Article


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.

Publication Date


  • 2014

Citation


  • Dung, D. Hoang. & Lucchini, A. (2014). Rationality of the probabilistic zeta functions of finitely generated profinite groups. Journal of Group Theory, 17 (2), 317-335.

Scopus Eid


  • 2-s2.0-84896774274

Number Of Pages


  • 18

Start Page


  • 317

End Page


  • 335

Volume


  • 17

Issue


  • 2

Place Of Publication


  • Germany

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.

Publication Date


  • 2014

Citation


  • Dung, D. Hoang. & Lucchini, A. (2014). Rationality of the probabilistic zeta functions of finitely generated profinite groups. Journal of Group Theory, 17 (2), 317-335.

Scopus Eid


  • 2-s2.0-84896774274

Number Of Pages


  • 18

Start Page


  • 317

End Page


  • 335

Volume


  • 17

Issue


  • 2

Place Of Publication


  • Germany