Normally ζ-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 ζ-reversible. We conjecture that these groups are pronilpotent and we prove this conjecture if...
Збережено в:
| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2016
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/155198 |
| Теги: |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Normally ζ-reversible profinite groups / L. Cimetta, A. Lucchini // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 24-50. — Бібліогр.: 21 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| 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 ζ-reversible. We conjecture that these groups are pronilpotent and we prove this conjecture if G is a normally ζ-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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