We generalize to FC*, the class of generalized FC-groups introduced in [F. de Giovanni, A. Russo, G. Vincenzi, Groups with restricted con- jugacy 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.

THE ENGEL ELEMENTS IN GENERALIZED FC-GROUPS

VINCENZI, Giovanni;TORTORA, ANTONIO
2014-01-01

Abstract

We generalize to FC*, the class of generalized FC-groups introduced in [F. de Giovanni, A. Russo, G. Vincenzi, Groups with restricted con- jugacy 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4521262
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