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6-BFC groups

Cliff David, James Wiegold (2006)

Rendiconti del Seminario Matematico della Università di Padova

FC-gruppi e proiettività

Carmela Musella (2001)

Bollettino dell'Unione Matematica Italiana

Some lattice properties of FC-groups and generalized FC-groups are considered in this paper.

Groups with complete lattice of nearly normal subgroups.

Maria De Falco, Carmela Musella (2002)

Revista Matemática Complutense

A subgroup H of a group G is said to be nearly normal in G if it has finite index in its normal closure in G. A well-known theorem of B.H. Neumann states that every subgroup of a group G is nearly normal if and only if the commutator subgroup G' is finite. In this article, groups in which the intersection and the join of each system of nearly normal subgroups are likewise nearly normal are considered, and some sufficient conditions for such groups to be finite-by-abelian are given.

Groups with nearly modular subgroup lattice

Francesco de Giovanni, Carmela Musella (2001)

Colloquium Mathematicae

A subgroup H of a group G is nearly normal if it has finite index in its normal closure H G . A relevant theorem of B. H. Neumann states that groups in which every subgroup is nearly normal are precisely those with finite commutator subgroup. We shall say that a subgroup H of a group G is nearly modular if H has finite index in a modular element of the lattice of subgroups of G. Thus nearly modular subgroups are the natural lattice-theoretic translation of nearly normal subgroups. In this article we...

Groups with Restricted Conjugacy Classes

de Giovanni, F., Russo, A., Vincenzi, G. (2002)

Serdica Mathematical Journal

Let F C 0 be the class of all finite groups, and for each nonnegative integer n define by induction the group class FC^(n+1) consisting of all groups G such that for every element x the factor group G/CG ( <x>^G ) has the property FC^n . Thus FC^1 -groups are precisely groups with finite conjugacy classes, and the class FC^n obviously contains all finite groups and all nilpotent groups with class at most n. In this paper the known theory of FC-groups is taken as a model, and it is shown that...

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