We are concerned with conditions under which a locally compact group G has a maximal compact normal subgroup K and whether or not G/K is a Lie group. If G has small compact normal subgroups K such that G/K is a Lie group, then G is pro-Lie. If in G there is a collection of closed normal subgroups {Ha} such that f~| Ha = e and G/Ha is a Lie group for each a, then G is a residual Lie group. We de...

Objective(s) The effect of Berberis vulgaris aqueous extract in hepatocarcinogenic rats was studied to investigate the apoptotic and sodium, potassium elements properties. A loss of both intracellular potassium and sodiumoccurs when apoptotic cells shrink and prior to the loss of membraneintegrity. Materials and Methods Forty-eight Sprague dawley rats were randomly divided into 2 groups, normal...

Skew morphisms, which generalise automorphisms for groups, provide a fundamental tool the study of regular Cayley maps and, more generally, finite groups with complementary factorisation $G=BY$, where $Y$ is cyclic and core-free in $G$. In this paper, we classify all examples $B$ monolithic (meaning that it has unique minimal normal subgroup, subgroup not abelian) As consequence, obtain classif...

OBJECTIVE To identify risk factors for normal-tension glaucoma among subgroups of patients. METHODS In 93 patients with unilateral normal-tension glaucoma, intereye comparison of baseline spherical equivalent, central corneal thickness, untreated intraocular pressure, disc area, and zone beta variables was performed among the following 4 subgroups classified according to age and visual field ...

Abstract We give sufficient conditions to ensure that the intersection of product two subgroups A and B a group G with an abelian normal subgroup K is .

Let π1(C) be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic p > 0 of countable cardinality. Let N be a normal (resp. characteristic) subgroup of π1(C). Under the hypothesis that the quotient π1(C)/N admits an infinitely generated Sylow p-subgroup, we prove that N is indeed isomorphic to a normal (resp. characteris...

in this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (k, ?) are equivalent. for a normal subgroup h of k, we define a weight function ?? on kih and obtain connection between left amenability of (k, ?) and (k|h, ??). let h be a compact subhypergroup of k. we define the weight function on k||h and obtain connection betw...

We construct the first examples of normal subgroups mapping class groups that are isomorphic to non-free right-angled Artin groups. Our construction also gives normal, other groups, such as braid and pure well many group, Torelli subgroup. work recovers generalizes seminal result Dahmani–Guirardel–Osin, which free, purely pseudo-Anosov give two applications our methods: (1) we produce an explic...