we give a new proof of the well known wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎we apply the concept of frobenius kernel in frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

some servers are to be located at nodes of a network. demand for services of these servers is located at each node and a subset of the nodes is to be chosen to locate one server in each. each customer selects a server with a probability dependent on distance and a certain amount of benefit is achieved after giving service to the customer. customers may waive receiving service with a known proba...

epilepsy is the most frequnt nearological affiction and afflicts 1% about of the worlds population. currently there is an urgent need for the development of novel anticonvulsants with higher levels of potency and lower levels of toxicity. in this paper, a series of new 6-(substituted-phenyl)thiazolo[3,2-b][1,2,4]triazole derivatives were synthesized and tested for their anticonvulsant activity ...

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

We prove that the number of minimal transversals (and also the number of maximal independent sets) in a 3-uniform hypergraph with n vertices is at most c, where c ≈ 1.6702. The best known lower bound for this number, due to Tomescu, is ad, where d = 10 1 5 ≈ 1.5849 and a is a constant.

Dynkin’s classification of maximal subalgebras of simple finite dimensional complex Lie algebras is generalized to matrix Lie superalgebras, i.e., the Lie subsuperalgebras of gl(p|q).

The trace of a family of sets A on a set X is A|X = {A ∩ X : A ∈ A}. If A is a family of k-sets from an n-set such that for any r-subset X the trace A|X does not contain a maximal chain, then how large can A be? Patkós conjectured that, for n sufficiently large, the size of A is at most ( n−k+r−1 r−1 ) . Our aim in this paper is to prove this conjecture.

We study the structure of the maximal ideal space M(H∞) of the algebra H ∞ = H∞(D) of bounded analytic functions defined on the open unit disk D ⊂ C. Based on the fact that dim M(H∞) = 2 we prove for H∞ the matrix-valued corona theorem. Our results heavily rely on the topological construction describing maximal ideal spaces of certain algebras of continuous functions defined on the covering spa...