Groups, in which almost all subgroups are near to normal
A subgroup H of a group G is said to be nearly normal, if H has a finite index in its normal closure. These subgroups have been introduced by B.H. Neumann. In a present paper is studied the groups whose non polycyclic by finite subgroups are nearly normal. It is not hard to show that under some n...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2004 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2004
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/156421 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Groups, in which almost all subgroups are near to normal / M.M. Semko, S.M. Kuchmenko // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 2. — С. 92–113. — Бібліогр.: 20 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | A subgroup H of a group G is said to be nearly
normal, if H has a finite index in its normal closure. These subgroups have been introduced by B.H. Neumann. In a present paper
is studied the groups whose non polycyclic by finite subgroups are
nearly normal. It is not hard to show that under some natural
restrictions these groups either have a finite derived subgroup or
belong to the class S₁F (the class of soluble by finite minimax
groups). More precisely, this paper is dedicated of the study of
S₁F groups whose non polycyclic by finite subgroups are nearly
normal.
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| ISSN: | 1726-3255 |