Clebsch–Gordan coefficients of discrete groups in subgroup bases

On $m^{th}$-autocommutator subgroup of finite abelian groups

Let $G$ be a group and $Aut(G)$ be the group of automorphisms of‎ ‎$G$‎. ‎For any natural‎ number $m$‎, ‎the $m^{th}$-autocommutator subgroup of $G$ is defined‎ ‎as‎: ‎$$K_{m} (G)=langle[g,alpha_{1},ldots,alpha_{m}] |gin G‎,‎alpha_{1},ldots,alpha_{m}in Aut(G)rangle.$$‎ ‎In this paper‎, ‎we obtain the $m^{th}$-autocommutator subgroup of‎ ‎all finite abelian groups‎.

Relative non-Normal Graphs of a Subgroup of Finite Groups

Let G be a finite group and H,K be two subgroups of G. We introduce the relative non-normal graph of K with respect to H , denoted by NH,K, which is a bipartite graph with vertex sets HHK and KNK(H) and two vertices x ∈ H HK and y ∈ K NK(H) are adjacent if xy / ∈ H, where HK =Tk∈K Hk and NK(H) = {k ∈ K : Hk = H}. We determined some numerical invariants and state that when this graph is planar or...

Structural Properties of Inner Amenable Discrete Groups

A SHORT NOTE ON ATOMS AND COATOMS IN SUBGROUP LATTICES OF GROUPS

In this paper we give an elementary argument about the atoms and coatoms of the latticeof all subgroups of a group. It is proved that an abelian group of finite exponent is strongly coatomic.

Additive Bases in Groups

We study the problem of removing an element from an additive basis in a general abelian group. We introduce analogues of the classical functions X,S and E (defined in the case of N) and obtain bounds on them. Our estimates on the functions SG and EG are valid for general abelian groups G while in the case of XG we show that distinct types of behaviours may occur depending on G.