We prove that every finite group $G$ contains a three-generated subgroup $H$ with the following property‎: ‎a prime $p$ divides the degree of an irreducible character of $G$ if and only if it divides the degree of an ...

The structure of groups which have at most two isomorphism classes of central factors ($B_2$-groups) are investigated‎. ‎A complete description of $B_2$-groups is obtained in the locally finite case and in the nilpotent ...

We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework ...

This paper deals with the mutual relationships between the factor group $G/zeta(G)$ (respectively $G/zeta_k(G)$) and $G'$ (respectively $gamma_{k+1}(G)$ and $G^{mathfrak{N}}$). It is proved that if $G/zeta(G)$ (respectively ...

A group class ${ X}$ is said to be countably recognizable if a group belongs to ${X}$ whenever all its countable subgroups lie in ${X}$‎. ‎It is proved here that most of the relevant classes of groups defined by restrictions ...