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Algebra and Discrete Mathematics, 2016, Volume 21, Issue 1, Pages 24–50
(Mi adm552)
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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
Normally $\zeta$-reversible profinite groups
Leone Cimetta, Andrea Lucchini Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121 Padova, Italy
Abstract:
We examine (finitely generated) profinite groups in which two formal Dirichlet series, the normal subgroup zeta function and the normal probabilistic zeta function, coincide; we call these groups normally $\zeta$-reversible. We conjecture that these groups are pronilpotent and we prove this conjecture if $G$ is a normally $\zeta$-reversible satisfying one of the following properties: $G$ is prosoluble, $G$ is perfect, all the nonabelian composition factors of $G$ are alternating groups.
Keywords:
profinite groups, Dirichlet series.
Received: 31.12.2015
Citation:
Leone Cimetta, Andrea Lucchini, “Normally $\zeta$-reversible profinite groups”, Algebra Discrete Math., 21:1 (2016), 24–50
Linking options:
https://www.mathnet.ru/eng/adm552 https://www.mathnet.ru/eng/adm/v21/i1/p24
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Abstract page: | 255 | Full-text PDF : | 93 | References: | 59 |
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