Let G be a countable Abelian group with Zd as a subgroup so that G/Zd is a locally finite group. (An Abelian group is locally finite if every element has finite order.) We can construct a rank one action of G so that the Z-subaction is 2-simple, 2-mixing and only commutes with the other transformations in the action of G. Applications of this construction include a transformation with square ro...

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

in this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...

An arithmetical structure on a finite, connected graph without loops is given by an assignment of positive integers to the vertices such that, at each vertex, integer there divisor sum adjacent vertices, counted with multiplicity if not simple. Associated finite abelian group known as its critical group. Keyes and Reiter gave operation that takes in produces one fewer vertex. We study how this ...

1 Multiply transitive groups Theorem 1.1. Let Ω be a finite set and G ≤ Sym(Ω) be 2–transitive. Let N E G be a minimal normal subgroup. Then one of the following holds: (a) N is regular and elementary abelian. (b) N is primitive, simple and not abelian. Proof. First we show that N is unique. Suppose that M is another minimal normal subgroup of G, so N ∩M = {e} and therefore [N,M ] = {e}. Since ...

Graded-division algebras are building blocks in the theory of finite-dimensional associative graded by a group G. If G is abelian, they can be described, using loop construction, terms central simple graded-division algebras. On other hand, given finite abelian G, any G-graded-division algebra over field F determined, thanks to result Picco and Platzeck, its class (ordinary) Brauer isomorphism ...

For each Sophie Germain prime g≥5, we construct an absolutely simple polarized abelian variety of dimension g over a finite field, whose automorphism group is cyclic order 4g+2. We also provide description on the asymptotic behavior numbers that are related to our construction.

‎there are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{z}_{2}$ or $mathbb{z}_{15}$. still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of sylow $p$-subgroups for each prime $p$, etc. in this...

Let T be the set of minimal primes of a Krull domain A. If S is a subset of T9 we form B = n AP for PeS and study the relation of the class group of B to that of A. We find that the class group of B is always a homomorphic image of that of A. We use this type of construction to obtain a Krull domain with specified class group and then alter such a Krull domain to obtain a Dedekind domain with t...