intersections of prefrattini subgroups in finite soluble groups

Intersections of Analytically and Geometrically Finite Subgroups of Kleinian Groups

We consider the intersection of pairs of subgroups of a Kleinian group of the second kind K whose limit sets intersect, where one subgroup G is analytically finite and the other J is geometrically finite, possibly infinite cyclic. In the case that J is infinite cyclic generated by M , we show that either some power of M lies in G or there is a doubly cusped parabolic element Q of G with the sam...

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.

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 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.

CENTRALISERS OF FINITE SUBGROUPS IN SOLUBLE GROUPS OF TYPE FPn

We show that for soluble groups of type FPn, centralisers of finite subgroups need not be of type FPn.

Subgroups of Finite Groups