The goal of this paper is to study finite groups admitting a pseudocomplemented subgroup lattice (PK-groups) or a pseudocomplemented normal subgroup lattice (PKN-groups). In particular, we obtain a complete classification of finite PK-groups and of finite nilpotent PKN-groups. We also study groups with a Stone normal subgroup lattice, and we classify finite groups for which every subgroup has a...

In this paper we continue the study of intuitionistic fuzzy groups by introducing the notion of intuitionistic fuzzy normal subgroup based on intuitionistic fuzzy space as a generalization of fuzzy normal subgroup. MSC2000 : 20N25, 03E72. Key Word : Fuzzy space, intuitionistic fuzzy space, intuitionistic fuzzy group, normal intuitionistic fuzzy subgroup .

The goal of this survey is to study some classes of groups determined by different types of complementation of their normal subgroup lattices. The groups whose normal subgroup lattices are Stone lattices, boolean lattices or ortholattices will be also investigated. MSC (2000): Primary 20D30, Secondary 20E15, 06C15, 06D15.

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...

in this paper, we will give necessary and sufficient conditions for certain hnnextensions of subgroup separable groups with normal associated subgroup to be conjugacyseparable. in fact, we will show that these hnn extensions are conjugacy separable if and onlyif the normalizer of one of its associated subgroup is conjugacy separable.

A subgroup $H$ is said to be $nc$-supplemented in a group $G$ if there exists a subgroup $Kleq G$ such that $HKlhd G$ and $Hcap K$ is contained in $H_{G}$, the core of $H$ in $G$. We characterize the supersolubility of finite groups $G$ with that every maximal subgroup of the Sylow subgroups is $nc$-supplemented in $G$.