Results 1 to 10 of about 134 (134)

The Engel elements in generalized FC-groups [PDF]

Illinois Journal of Mathematics, 2014
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]

Bulletin of the Australian Mathematical Society, 2010
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

Journal of Algebra, 2011
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

Siberian Mathematical Journal, 2015
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]

, 2007
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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Some topics in the theory of generalized fc-groups

, 2011
A finiteness condition is a group-theoretical property which is possessed by all finite groups: thus it is a generalization of finiteness. This embraces an immensely wide collection of properties like, for example, finiteness, finitely generated, the maximal condition and so on. There are also numerous finiteness conditions which restrict, in some way,
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On generalized FC-groups

Journal of Group Theory, 2008
Let \(D_i\) be the class of groups with \(i\) conjugacy classes of infinite size and let \(D\) be the union of all \(D_i\) for all \(i=0,1,2,\dots\). In these terms \(D_0\) is exactly the class of FC-groups. In this article the authors investigate the \(D\)-groups.
M. HERZOG, LONGOBARDI, Patrizia, MAJ, Mercede   +2 more
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On the Wielandt subgroup of generalized FC-groups

International Journal of Algebra and Computation, 2014
We extend to soluble FC*-groups, the class of generalized FC-groups introduced in [de Giovanni, Russo and Vincenzi, Groups with restricted conjugacy classes, Serdica Math. J. 28(3) (2002) 241–254], the characterization of finite soluble T-groups, and some results on the Wielandt subgroup, obtained recently in [Kaplan, On finite T-groups and the ...
G. Kaplan, VINCENZI, Giovanni
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GROUPS WHOSE PROPER SUBGROUPS ARE GENERALIZED FC-GROUPS

Journal of Algebra and Its Applications, 2011
Let 𝔛 be a class of groups. A group G is said to be minimal non-𝔛 if all proper subgroups of G are 𝔛-groups but G itself is not. The aim of this paper is to study the class of minimal non-FCn-groups, where FCn(n is a positive integer) is a class of generalized FC-groups introduced in [F. de Giovanni, A. Russo and G.
Imperatore D., Russo A., Vincenzi G.
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Conjugately dense subgroups in generalized FC-groups.

2009
Summary: A subgroup \(H\) of a group \(G\) is called conjugately dense in \(G\) if \(H\) has nonempty intersection with each class of conjugate elements in \(G\). The knowledge of conjugately dense subgroups is related with an unsolved problem in group theory, as testified in the Kourovka Notebook.
Erfanian, A, RUSSO, Francesco
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