In this paper, we study the complete ⋆-metric semigroups and groups Raǐkov completion of invariant groups. We obtain following. (1) Let (X,d⋆) be a space containing semigroup (group) G that is dense subset X. If restriction d⋆ on invariant, then X can become as subgroup, (2) (G,d⋆) group such G. Then, if only (G,τd⋆) complete.

In this paper we study the structure of locally solvable, solvable, locally nilpotent, and nilpotent maximal subgroups of skew linear groups. In [S. Akbari et al., J. Algebra 217 (1999) 422–433] it has been conjectured that if D is a division ring and M a nilpotent maximal subgroup of D∗, then D is commutative. In connection with this conjecture we show that if F [M]\F contains an algebraic ele...

Kulikov has exhibited an étale morphism F : X → Cn of degree d > 1 which is surjective modulo codimension two with X simply connected, settling his generalized jacobian problem. His method reduces the problem to finding a hypersurface D ⊂ Cn and a subgroup G ⊂ π1(C − D) of index d generated by geometric generators. By contrast we show that if D has simple normal crossings away from a set of cod...

In a 1985 paper, Berthold J. Maier gave necessary and sufficient conditions for the weak embeddability of amalgams of two nilpotent groups of class two over a common subgroup. Then he derived simpler conditions for some special cases. One of his subsequent results is incorrect, and we provide a counterexample. Finally, we provide a fix for the result. In this note, N2 denotes the variety of nil...

We study the group of automorphisms of Shimura curves X0(D,N) attached to an Eichler order of square-free level N in an indefinite rational quaternion algebra of discriminant D > 1. We prove that, when the genus g of the curve is greater than or equal to 2, Aut(X0(D,N)) is a 2-elementary abelian group which contains the group of Atkin-Lehner involutions W0(D,N) as a subgroup of index 1 or 2. It...

Background: The prevalence of hypertension in patients with type 2 diabetes (T2D) is approximately twice as much as healthy people. This study was designed to determine the effect of L-arginine supplementation on blood pressure in patients with T2D. Methods: In a double-blind randomized clinical trial, 75 T2D were randomly divided into three groups (3 g/d and 6g/d of L-arginine and placebo) for...

For any positive integer N, we completely determine the structure of rational cuspidal divisor class group X0(N), which is conjecturally equal to torsion subgroup J0(N). More specifically, for a given prime ℓ, construct Zℓ(d) non-trivial d N. Also, compute order linear equivalence and show that ℓ-primary X0(N) isomorphic direct sum cyclic subgroups generated by classes Zℓ(d).

If P is a p-group for some prime p we shall write M (P ) to denote the set of all maximal subgroups of P and Md(P ) = {P1, ..., Pd} to denote any set of maximal subgroups of P such that ∩d i=1 Pi = Φ(P ) and d is as small as possible. In this paper, the structure of a finite group G under some assumptions on the c-normal or s-quasinormally embedded subgroups in Md(P ), for each prime p, and Syl...

In this paper, a von Neumann-type inequality is studied on an Eaton triple $ (V,G,D) $, where V real inner product space, G compact subgroup of the orthogonal group O (V) and D \subset closed convex cone. By using structure triple, refinement shown. special case = ( ) Cauchy-Schwarz obtained.