A NOTE ON NILPOTENT-BY-ČERNIKOV GROUPS

A NOTE ON NILPOTENT-BY-ČERNIKOV GROUPS

In this note we prove that a locally graded group $G$ in which all proper subgroups are (nilpotent of class not exceeding $n$)-by-Černikov, is itself (nilpotent of class not exceeding $n$)-by-Černikov. As a preparatory result that is used for the proof of the former statement in the case of a period...

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Veröffentlicht in:Glasgow mathematical journal 2004-05, Vol.46 (2), p.211-215
Hauptverfasser: BRUNO, BRUNELLA, NAPOLITANI, FRANCO
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description In this note we prove that a locally graded group $G$ in which all proper subgroups are (nilpotent of class not exceeding $n$)-by-Černikov, is itself (nilpotent of class not exceeding $n$)-by-Černikov. As a preparatory result that is used for the proof of the former statement in the case of a periodic group, we also prove that a group $G$, containing a nilpotent of class $n$ subgroup of finite index, also contains a characteristic subgroup of finite index that is nilpotent of class not exceeding $n$.
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title A NOTE ON NILPOTENT-BY-ČERNIKOV GROUPS
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