for a finite group $g$ let $nu(g)$ denote the number of conjugacy classes of non-normal subgroups of $g$. we give a short proof of a theorem of brandl, which classifies finite groups with $nu(g)=1$.

In this paper, the notions of   , q  -Q-fuzzy subgroup and normal subgroup are introduced and some of their properties are investigated.

The theory of fuzzy sets was inspired by Zadeh [10]. Subsequently, Rosenfeld introduced the concept of a fuzzy subgroup of a group [9]. Fuzzy cosets and fuzzy normal subgroups of a group G have been studied in [3, 5, 8]. In [4], the ring of cosets of a fuzzy ideal was constructed. Let A and B be fuzzy subgroups of G such that B ⊆ A. The purpose of this paper is to introduce the notion of fuzzy ...

a subgroup $x$ of a group $g$ is almost normal if the index $|g:n_g(x)|$ is finite, while $x$ is nearly normal if it has finite index in the normal closure $x^g$. this paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.