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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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2016
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/137 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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. |
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