Local nilpotent groups satisfying a weak condition of minimality or maximality for subgroups of fixed degree of nilpotency
We study locally nilpotent groups containing subgroups of class $c, c>1$, and satisfying the weak maximum condition or the weak minimum condition on $с$-nilpotent subgroups. It is proved that nilpotent groups of this type are minimax and periodic locally nilpotent groups of this type are...
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| Date: | 1992 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8107 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We study locally nilpotent groups containing subgroups of class $c, c>1$, and satisfying the weak maximum condition or the weak minimum condition on $с$-nilpotent subgroups. It is proved that nilpotent groups of this type are minimax and periodic locally nilpotent groups of this type are Chernikov groups. It is also proved that if a group $G$  is either nilpotent or periodic locally nilpotent and if all of its $с$-nilpotent subgroups are of finite rank, then $G$  is of finite rank. If $G$  is a non-periodic locally nilpotent group, these results, in general, are not valid. |
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