in this paper, we examine that some simple $k_4$-groups can be determined uniquely by their orders and one or two irreducible complex character degrees.

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...

Notation and Terminology. Given a finite lattice L, the expression L ∼= [H,G] means “there exist finite groups H < G such that L is isomorphic to the interval {K | H 6 K 6 G} in the subgroup lattice of G.” A group G is called almost simple if G has a normal subgroup S P G which is nonabelian, simple, and has trivial centralizer, CG(S) = (e). If H 6 G, then the core of H in G, denoted coreG(H), ...

In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of ‎‎, for any multiplication subset S of...

We provide a Rademacher theorem for intrinsically Lipschitz functions \(\phi\colon U\subseteq\mathbf{W}\to\mathbf{L}\), where \(U\) is Borel set, \(\mathbf{W}\) and \(\mathbf{L}\) are complementary subgroups of Carnot group, we require that normal subgroup. Our hypotheses satisfied example when horizontal Moreover, an area formula this class functions.