The Engel elements in generalized FC-groups
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2014
- DOI:
- 10.48550/arXiv.1412.6353
- arXiv:
- arXiv:1412.6353
- Bibcode:
- 2014arXiv1412.6353T
- Keywords:
-
- Mathematics - Group Theory;
- 20F45;
- 20F24
- E-Print:
- to appear in "Illinois Journal of Mathematics"