Generalization of Hamiltonian groups
The following properties are considered: (CO) the core of every subgroup \(H\) of \(G\) is the irredundant intersection of the distinct conjugates of \(H\) and (NC) the normal closure of every subgroup of \(H\) is irredundantly generated by the distinct conjugates of \(H\). It is shown that each of these properties is equivalent to every subgroup of \(G\) having at most 2 conjugates. Such groups are nilpotent and centre-by-finite.
scientific article; zbMATH DE number 411639