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arXiv · 1412.6353

The Engel elements in generalized FC-groups

A. Tortora·G. Vincenzi
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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.

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A. Tortora, G. Vincenzi. 2014-12-19. The Engel elements in generalized FC-groups. https://arxiv.org/abs/1412.6353

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