Conjugately dense subgroups in generalized $FC$-groups
Conjugately dense subgroups in generalized $FC$-groups
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. Here we point out the role of conjugately dense subgroups in generalized FC-groups, generalized soluble groups and generalized nilpotent groups.
- University of Palermo Italy
generalized nilpotent groups, generalized soluble groups, generalized FC-groups, FC-groups and their generalizations, Generalizations of solvable and nilpotent groups, Chains and lattices of subgroups, subnormal subgroups, conjugately dense subgroups, Subgroup theorems; subgroup growth, FC-groups; coverings, Conjugacy classes for groups, conjugacy classes
generalized nilpotent groups, generalized soluble groups, generalized FC-groups, FC-groups and their generalizations, Generalizations of solvable and nilpotent groups, Chains and lattices of subgroups, subnormal subgroups, conjugately dense subgroups, Subgroup theorems; subgroup growth, FC-groups; coverings, Conjugacy classes for groups, conjugacy classes
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