Topologically Locally Finite Groups with a CC-Subgroup

TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

On the Irreducibility of Locally Analytic Principal Series Representations

Let G be a p-adic connected reductive group with Lie algebra g. For a parabolic subgroup P ⊂ G and a finite-dimensional locally analytic representation V of a Levi subgroup of P, we study the induced locally analytic G-representation W = IndP (V ). Our result is the following criterion concerning the topological irreducibility of W : If the Verma module U(g) U(p) V ′ associated to the dual repr...

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

ON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS

Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...

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 $G$.