The Engel elements in generalized FC-groups [PDF]
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 ...
Vincenzi Giovanni, Tortora Antonio.
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PRONORMALITY IN GENERALIZEDFC-GROUPS [PDF]
AbstractWe extend some results known forFC-groups to the classFC*of generalizedFC-groups introduced in de Giovanniet al.[‘Groups with restricted conjugacy classes’,Serdica Math. J.28(3) (2002), 241–254]. The main theorems pertain to the join of pronormal subgroups. The relevant role that the Wielandt subgroup plays in anFC*-group is pointed out.
ROMANO, EMANUELA, VINCENZI, Giovanni
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On the theory of generalized FC-groups
For each non-negative integer \(n\), the group class \(\text{FC}^n\) can be defined recursively in the following way: \(\text{FC}^0\) is the class of all finite groups, and a group \(G\) belongs to \(\text{FC}^{n+1}\) if \(G/C_G(\langle x\rangle^G)\) is an \(\text{FC}^n\)-group for every element \(x\) of \(G\).
Robinson D. J. S., Russo A., Vincenzi G.
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Generalized FC-groups with chain conditions
Recall that the FC-centre of a group \(G\) is the subgroup consisting of all elements with only finitely many conjugates, and \(G\) is an FC-group if it coincides with the FC-centre, i.e. if \(G\) has finite conjugacy classes. If \(c\) is any positive integer, a group \(G\) is called an \(\mathrm{FC}_c\)-group if the \(c\)-th term \(\gamma_c(G)\) of ...
Zhang, Zh., Chen, Sh.
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Generalized FC-groups in Finitary Groups [PDF]
A group $G$ is called $FC$-group if it is a group in which each element has finitely many conjugates. This condition is equivalent to require that $G/C_G(x^G)$ is a finite group for each element $x$ of $G$, where the symbol $x^G$ denotes the normal closure of the subgroup $\langle x \rangle$ in $G$. A group $G$ is called $CC$-group if $G/C_G(x^G)$ is a
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