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A NOTE ON NILPOTENT-BY-ČERNIKOV GROUPS

Published online by Cambridge University Press:  19 May 2004

BRUNELLA BRUNO  and
FRANCO NAPOLITANI
BRUNELLA BRUNO
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7, 35131 Padova (Italy) e-mail: bruno@math.unipd.it, napolita@math.unipd.it
FRANCO NAPOLITANI
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7, 35131 Padova (Italy) e-mail: bruno@math.unipd.it, napolita@math.unipd.it
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Abstract

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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 $n$.

Keywords

Primary 20F19Secondary 20F22
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 46 , Issue 2 , May 2004 , pp. 211 - 215
Copyright
2004 Glasgow Mathematical Journal Trust