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Summer 2014 The Engel elements in generalized FC-groups
Antonio Tortora, Giovanni Vincenzi
Illinois J. Math. 58(2): 577-583 (Summer 2014). DOI: 10.1215/ijm/1436275499


We generalize to $FC^{*}$, the class of generalized $FC$-groups introduced in [ 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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Antonio Tortora. Giovanni Vincenzi. "The Engel elements in generalized FC-groups." Illinois J. Math. 58 (2) 577 - 583, Summer 2014.


Received: 17 June 2014; Revised: 14 November 2014; Published: Summer 2014
First available in Project Euclid: 7 July 2015

zbMATH: 1329.20046
MathSciNet: MR3367664
Digital Object Identifier: 10.1215/ijm/1436275499

Primary: 20F24, 20F45

Rights: Copyright © 2014 University of Illinois at Urbana-Champaign


Vol.58 • No. 2 • Summer 2014
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