A new characterization of groups with central chief factors

Orlando Stanley Juriaans, Deborah Martins Raphael


In [1] it is proved that a locally nilpotent group is an \((X)\)-group arising the question whether the converse holds. In this paper we derive some interesting properties and give a complete characterization of \((X)\)-groups. As a consequence we obtain a new characterization of groups whose chief factors are central and it follows also that there exists an \((X)\)-group which is not locally nilpotent, thus answering the question raised in [1]. We also prove a resultĀ  which extends one on finitely generated nilpotent groups due to Gruenberg.


\((X)\)-group, nilpotent, residually central, Z-group

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