‎In this survey we highlight the relations between some subgroup embedding properties that characterise groups in which normality is a transitive relation in‎ ‎certain universes of groups with some finiteness properties‎.

Let $G$ be a finite group and let $mathcal{P}=P_{1},ldots,P_{m}$ be a sequence‎ ‎of Sylow $p_{i}$-subgroups of $G$‎, ‎where $p_{1},ldots,p_{m}$ are the distinct‎ ‎prime divisors of $leftvert Grightvert $‎. ‎The Sylow ...

‎The aim of this survey article is to present some structural results about of groups whose Sylow p-subgroups are metacylic (p a prime)‎. ‎A complete characterisation of non-nilpotent groups whose ...

Let $L$ be a free Lie algebra of rank $rgeq2$ over a field $F$ and let $L_n$ denote the degree $n$ homogeneous component of $L$‎. ‎By using the dimensions of the corresponding homogeneous and fine homogeneous components ...

We report on fi nite groups having square-free conjugacy class sizes, in particular in the framework of factorised groups.

An isomorphism between the group ring of a finite group and a ring of certain block diagonal matrices is established. It is shown that for any group ring matrix $A$ of $mathbb{C} G$ there exists a matrix $U$ (independent ...