in this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. explicit formulas are givenfor dihedral groups $d_{2n}$, quasi-dihedral groups $qd_{2^n}$, generalized quaternion groups $q_{4n}$ and modular $p$-groups $m_{p^n}$.

in this paper we find systems of subgroups of a finite‎ ‎group‎, ‎which $bbb p$-subnormality guarantees supersolvability‎ ‎of the whole group‎.

a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the center of such...

in this paper we find systems of subgroups of a finite‎ ‎group‎, ‎which $bbb p$nobreakdash-hspace{0pt}subnormality guarantees supersolvability‎ ‎of the whole group‎.

let $g$ be a non-abelian group of order $p^n$‎, ‎where $nleq 5$ in which $g$ is not extra special of order $p^5$‎. ‎in this paper we determine the maximal size of subsets $x$ of $g$‎ ‎with the property that $xyneq yx$ for any $x,y$ in $x$ with‎ ‎$xneq y$‎.