the nc-supplemented subgroups of finite groups

The nc-supplemented subgroups of finite groups

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 $G$.

Classifying fuzzy normal subgroups of finite groups

In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.

CLASSIFYING FUZZY SUBGROUPS OF FINITE NONABELIAN GROUPS

In this paper a rst step in classifying the fuzzy subgroups of a nite nonabelian group is made. We develop a general method to count the number of distinct fuzzy subgroups of such groups. Explicit formulas are obtained in the particular case of dihedral groups.

ON c-SUPPLEMENTED MAXIMAL AND MINIMAL SUBGROUPS OF SYLOW SUBGROUPS OF FINITE GROUPS

This paper proves: Let F be a saturated formation containing U . Suppose that G is a group with a normal subgroup H such that G/H ∈ F . (1) If all maximal subgroups of any Sylow subgroup of F ∗(H) are c-supplemented in G, then G ∈ F ; (2) If all minimal subgroups and all cyclic subgroups with order 4 of F ∗(H) are c-supplemented in G, then G ∈ F .

Subgroups of Finite Groups

On $Phi$-$tau$-quasinormal subgroups of finite groups

‎Let $tau$ be a subgroup functor and $H$ a $p$-subgroup of a finite group $G$‎. ‎Let $bar{G}=G/H_{G}$ and $bar{H}=H/H_{G}$‎. ‎We say that $H$ is $Phi$-$tau$-quasinormal in $G$ if for some $S$-quasinormal subgroup $bar{T}$ of $bar{G}$ and some $tau$-subgroup $bar{S}$ of $bar{G}$ contained in $bar{H}$‎, ‎$bar{H}bar{T}$ is $S$-quasinormal in $bar{G}$ and $bar{H}capbar{T}leq bar{S}Phi(bar{H})$‎. ‎I...