abstract. in this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

The complex fuzzy environment is an innovative tool to handle ambiguous situations in different mathematical problems. In this article, we commence the abstraction of (?,?)-complex sets, subgroupoid, subgroups and describe important examples symmetric group under sets. Additionally, discuss conjugacy class with respect normal subgroups. We define cosets elaborate upon certain operation analog t...

The notion of an n-ary group is a natural generalization of the notion of a group and has many applications in different branches. In this paper, the notion of (normal) fuzzy n-ary subgroup of an n-ary group is introduced and some related properties are investigated. Characterizations of fuzzy n-ary subgroups are given.

This article computes the number of fuzzy subgroups of symmetric group S4 and constructs some of them. First, an equivalence relation on the set of all fuzzy subgroups of a group G is defined. The diagram of subgroups lattice of S4 is used to determine the number of fuzzy subgroups of S4. We find the total number of fuzzy subgroups of S4 is 220. Mathematics Subject Classification: 20B30, 20B35,...

In this study, firstly, we interpret the level set, support, kernel for bipolar complex fuzzy (BCF) characteristic function, and BCF point. Then, subgroup, normal conjugate, normalizer cosets, abelian factor group. Furthermore, present associated examples theorems, prove these theorems. After that, image pre-image of subgroups under homomorphism related

‎let $g$ be a finite group and let $n$ be a normal subgroup of $g$‎. ‎suppose that ${rm{irr}} (g | n)$ is the set of the irreducible characters of $g$ that contain $n$ in their kernels‎. ‎in this paper‎, ‎we classify solvable groups $g$ in which the set $mathcal{c} (g) = {{rm{irr}} (g | n) | 1 ne n trianglelefteq g }$ has at most three elements‎. ‎we also compute the set $mathcal{c}(g)$ for suc...