2014/12/19 by A. Tortora, Antonio Tortora, Tortora, A. +3
Mathematics · Medicine · #20F24 #20F45 #Advanced Topics in Algebra #Chronic Lymphocytic Leukemia Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR #msc:20F24 #msc:20F45
paper · pdf · doi:10.48550/arxiv.1412.6353
to appear in "Illinois Journal of Mathematics"
arxiv created 2014/12/19 · openalex publication_date 2014/12/19 · arxiv updated 2014/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.