The Engel elements in generalized FC-groups
Group Theory
2014-12-22 v1
Abstract
We generalize to FC*, the class of generalized FC-groups introduced in [F. de Giovanni, A. Russo, G. Vincenzi, Groups with restricted conjugacy classes, Serdica Math. J. 28 (2002), 241-254], a result of Baer on Engel elements. More precisely, we prove that the sets of left Engel elements and bounded left Engel elements of an FC*-group G coincide with the Fitting subgroup; whereas the sets of right Engel elements and bounded right Engel elements of G are subgroups and the former coincides with the hypercentre. We also give an example of an FC*-group for which the set of right Engel elements contains properly the set of bounded right Engel elements.
Cite
@article{arxiv.1412.6353,
title = {The Engel elements in generalized FC-groups},
author = {A. Tortora and G. Vincenzi},
journal= {arXiv preprint arXiv:1412.6353},
year = {2014}
}
Comments
to appear in "Illinois Journal of Mathematics"