The aim of this paper is basically to study some of the standard properties of the intuitionistic fuzzy subgroups under a crisp map. Also, we study some properties of intuitionistic fuzzy normal subgroups.

Maximal and minimal conditions for ideals in associative rings have often been considered, but little seems to be known of these conditions in non-associative rings, or of chain conditions on the non-normal subgroups of a group. Moreover, it is usual to assume the condition for one-sided ideals in noncommutative rings, and the weaker condition for two-sided ideals rarely appears. In this note w...

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

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 $nu(g)=1$.

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

In this paper we prove that if G is a group for which there are k non-Frattini chief factors isomorphic to characteristically simple A, then has normal section C/R the direct product of minimal subgroups G/R A. This significant extension notion crown factors.

We study the topological structure and dynamics of groups homeomorphisms scattered spaces. For a large class them (including homeomorphism group any ordinal space or locally compact space), we establish Roelcke-precompactness amenability, classify all closed normal subgroups compute universal minimal flow. As by-product, up to isomorphism