Normally \(\zeta\)-reversible profinite groups
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 conjec...
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| Date: | 2016 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2016
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/137 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543134465392640 |
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| author | Cimetta, Leone Lucchini, Andrea |
| author_facet | Cimetta, Leone Lucchini, Andrea |
| author_sort | Cimetta, Leone |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2016-05-11T05:58:01Z |
| description | 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. |
| first_indexed | 2026-02-08T07:57:40Z |
| format | Article |
| id | admjournalluguniveduua-article-137 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:40Z |
| publishDate | 2016 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-1372016-05-11T05:58:01Z Normally \(\zeta\)-reversible profinite groups Cimetta, Leone Lucchini, Andrea profinite groups, Dirichlet series 20E07 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. Lugansk National Taras Shevchenko University 2016-05-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/137 Algebra and Discrete Mathematics; Vol 21, No 1 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/137/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/137/68 Copyright (c) 2016 Algebra and Discrete Mathematics |
| spellingShingle | profinite groups Dirichlet series 20E07 Cimetta, Leone Lucchini, Andrea Normally \(\zeta\)-reversible profinite groups |
| title | Normally \(\zeta\)-reversible profinite groups |
| title_full | Normally \(\zeta\)-reversible profinite groups |
| title_fullStr | Normally \(\zeta\)-reversible profinite groups |
| title_full_unstemmed | Normally \(\zeta\)-reversible profinite groups |
| title_short | Normally \(\zeta\)-reversible profinite groups |
| title_sort | normally \(\zeta\)-reversible profinite groups |
| topic | profinite groups Dirichlet series 20E07 |
| topic_facet | profinite groups Dirichlet series 20E07 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/137 |
| work_keys_str_mv | AT cimettaleone normallyzetareversibleprofinitegroups AT lucchiniandrea normallyzetareversibleprofinitegroups |