Geodesic
A new characterization of groups with central chief factors
Algebra and discrete mathematics, no. 3 (2009), pp. 62-68.

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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 result which extends one on finitely generated nilpotent groups due to Gruenberg.
Keywords: nilpotent, residually central
Mots-clés : $(X)$-group, Z-group. 
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     title = {A new characterization of groups with central chief factors},
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Orlando Stanley Juriaans; Deborah Martins Raphael. A new characterization of groups with central chief factors. Algebra and discrete mathematics, no. 3 (2009), pp. 62-68. http://geodesic.mathdoc.fr/item/ADM_2009_3_a5/