On the locally nilpotent groups with a centralisator of the finite rank
Locally nilpotent groups in which the centralizer of some finitely generated subgroup has finite rank are studied. It is shown that if $G$ is such a group and $F$ is a finitely generated subgroup with centralizer $C_G(F)$ of finite rank, then the centralizer of the image of $F$ in the factor group $...
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| Datum: | 1992 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8253 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Locally nilpotent groups in which the centralizer of some finitely generated subgroup has finite rank are studied. It is shown that if $G$ is such a group and $F$ is a finitely generated subgroup with centralizer $C_G(F)$ of finite rank, then the centralizer of the image of $F$ in the factor group $G /t (G)$ modulo the periodic part $t (G)$ also has finite rank. It is also shown that $G$  is hypercentral when F is cyclic and either $G$  is torsion-free or all Sylow subgroups of the periodic part of $C_G(F)$ are finite. |
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