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A finiteness condition on the coefficients of the probabilistic zeta function

Journal Article


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Abstract


  • We discuss whether finiteness properties of a profinite group G can be deduced from the coefficients 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.

Publication Date


  • 2013

Citation


  • Duong, D. Hoang. & Lucchini, A. (2013). A finiteness condition on the coefficients of the probabilistic zeta function. International Journal of Group Theory, 2 (1), 167-174.

Ro Full-text Url


  • https://ro.uow.edu.au/cgi/viewcontent.cgi?article=2995&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/1991

Number Of Pages


  • 7

Start Page


  • 167

End Page


  • 174

Volume


  • 2

Issue


  • 1

Place Of Publication


  • Iran, Islamic Republic of

Abstract


  • We discuss whether finiteness properties of a profinite group G can be deduced from the coefficients 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.

Publication Date


  • 2013

Citation


  • Duong, D. Hoang. & Lucchini, A. (2013). A finiteness condition on the coefficients of the probabilistic zeta function. International Journal of Group Theory, 2 (1), 167-174.

Ro Full-text Url


  • https://ro.uow.edu.au/cgi/viewcontent.cgi?article=2995&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/1991

Number Of Pages


  • 7

Start Page


  • 167

End Page


  • 174

Volume


  • 2

Issue


  • 1

Place Of Publication


  • Iran, Islamic Republic of