a subgroup $h$ is said to be $s$-permutable in a group $g$‎, ‎if‎ ‎$hp=ph$ holds for every sylow subgroup $p$ of $g$‎. ‎if there exists a‎ ‎subgroup $b$ of $g$ such that $hb=g$ and $h$ permutes with every‎ ‎sylow subgroup of $b$‎, ‎then $h$ is said to be $ss$-quasinormal in‎ ‎$g$‎. ‎in this paper‎, ‎we say that $h$ is a weakly $ss$-quasinormal‎ ‎subgroup of $g$‎, ‎if there is a normal subgroup ...

a result of dixon‎, ‎evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $g$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $g$ has finite rank‎. ‎it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator s...

The five highly related envelope subgroups of the avian sarcoma and leukosis viruses (ASLVs), subgroup A [ASLV(A)] to ASLV(E), are thought to have evolved from an ancestral envelope glycoprotein yet utilize different cellular proteins as receptors. Alleles encoding the subgroup A ASLV receptors (Tva), members of the low-density lipoprotein receptor family, and the subgroup B, D, and E ASLV rece...

A subgroup of a group is known as a surface subgroup if it is isomorphic to the fundamental group of a closed connected orientable surface with positive genus. The surface subgroup conjecture in low-dimensional topology proposes that if the fundamental group of a closed orientable irreducible 3-manifold is infinite, then it contains a surface subgroup. With the recent solution to the geometrisa...

in this article we introduce the notion of n-capable groups. it is shown that every group g admits a uniquely determined subgroup (〖z^n)〗^* (g) which is a characteristic subgroup and lies in the n-centre subgroup of the group g. this is the smallest subgroup of g whose factor group is n-capable. moreover, some properties of n-central extension will be studied.

a subgroup $h$ is said to be $s$-permutable in a group $g$‎, ‎if‎ ‎$hp=ph$ holds for every sylow subgroup $p$ of $g$‎. ‎if there exists a‎ ‎subgroup $b$ of $g$ such that $hb=g$ and $h$ permutes with every‎ ‎sylow subgroup of $b$‎, ‎then $h$ is said to be $ss$-quasinormal in‎ ‎$g$‎. ‎in this paper‎, ‎we say that $h$ is a weakly $ss$-quasinormal‎ ‎subgroup of $g$‎, ‎if there is a normal subgroup ...

A complex algebraic group G is in this note a subgroup of GL(n, C), the elements of which are all invertible matrices whose coefficients annihilate some set of polynomials {PM[Xn, • • • , X n n ]} in n 2 indeterminates. I t is said to be defined over a field KQC if the polynomials can be chosen so as to have coefficients in K. Given a subring B of C, we denote by GB the subgroup of elements of ...

In 1981, Thompson proved that, if n > 1 is any integer and G is any finite subgroup of GLn(C), then G has a semi-invariant of degree at most 4n2. He conjectured that, in fact, there is a universal constant C such that for any n ∈ N and any finite subgroup G < GLn(C), G has a semi-invariant of degree at most Cn. This conjecture would imply that the α-invariant αG(P), as introduced by Tian in 198...

‎let $h$ be a prefrattini subgroup of a soluble finite group $g$‎. ‎in the‎ ‎paper it is proved that there exist elements $x,y in g$ such that the equality‎ ‎$h cap h^x cap h^y = phi (g)$ holds‎.

a dummy variable technique that allows simultaneous study of subgroup combinations from the placebo and treatment groups. Medwxs and Results. In the placebo group (n=2,045), the low density lipoprotein cholesterol (LDL-C)/high density lipoprotein cholesterol (HDL-C) ratio was the best single predictor ofcardiac events. This ratio in combination with the serum triglyceride level revealed a high-...