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 $g$.

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...

We show that the biflatness—in the sense of A. Ya. Helemskĭı—of the Fourier algebra A(G) of a locally compact groupG forcesG to either have an abelian subgroup of finite index or to be non-amenable without containing F2 as a closed subgroup. An analogous dichotomy is obtained for biprojectivity.

A homogeneous space G/H is said to have a compact Clifford-Klein form if there exists a discrete subgroup Γ of G that acts properly discontinuously on G/H, such that the quotient space Γ\G/H is compact. When n is even, we find every closed, connected subgroup H of G = SO(2, n), such that G/H has a compact Clifford-Klein form, but our classification is not quite complete when n is odd. The work ...

Let G be a simple algebraic group over an algebraically closed field k of bad characteristic. We classify the spherical unipotent conjugacy classes of G. We also show that if the characteristic of k is 2, then the fixed point subgroup of every involutorial automorphism (involution) of G is a spherical subgroup of G.

Suppose G is an almost simple group containing a subgroup isomorphic to the three-dimensional Heisenberg group. For example any finite index subgroup of SL(3, Z) is such a group. The main result of this paper is that every action of G on a closed oriented surface by area preserving diffeomorphisms factors through a finite group.

Abstract. A homogeneous space G/H is said to have a compact Clifford-Klein form if there exists a discrete subgroup Γ of G that acts properly on G/H such that the quotient space Γ\G/H is compact. When n is even, we find every closed connected subgroup H of G = SO(2, n), such that G/H has a compact Clifford-Klein form, but our classification is not quite complete when n is odd. The work reveals ...

In this paper we introduce b− open, b− closed, quasi b− open, quasi b − closed, strongly b − open and strongly b − closed functions and investigate properties and characterizations of these new types of functions.

A sequence {un}n∈ω in abstract additively-written Abelian group G is called a T -sequence if there is a Hausdorff group topology on G relative to which limn un = 0. We say that a subgroupH of an infinite compact Abelian groupX is T -characterized if there is a T -sequence u = {un} in the dual group of X , such that H = {x ∈ X : (un, x) → 1}. We show that a closed subgroupH ofX is T -characteriz...