‎In this paper we present some results about subgroup which is‎ ‎generalization of the subgroup $R_{2}^{otimes}(G)={ain‎ ‎G|[a,g]otimes g=1_{otimes},forall gin G}$ of right‎ ‎$2_{otimes}$-Engel elements of a given group ...

‎The non-commuting graph $nabla(G)$ of a non-abelian group $G$ is defined as‎ ‎follows‎: ‎its vertex set is $G-Z(G)$ and two distinct vertices $x$ and $y$ are‎ ‎joined by an edge if and only if the commutator of $x$ and ...

‎Three infinite families of finite abelian groups will be‎ ‎described such that each member of these families has‎ ‎the R'edei $k$-property for many non-trivial values of $k$‎.

The number of factorizations of a finite abelian group as the product of two subgroups is computed in two different ways and a combinatorial identity involving Gaussian binomial coefficients is presented‎.