In this paper we study affine Coxeter groups. We show how to construct decompositions of the investigated groups into semi-direct products. We use this to give the complete list of irreducible representations of affine ...

A subgroup H of a finite group G is said to be Hall normally embedded in G if there is a normal subgroup N of G such that H is a Hall subgroup of N. A Schmidt group is a non-nilpotent finite group whose all proper ...

A vector balleans is a vector space over R en- dowed with a coarse structure in such a way that the vector opera- tions are coarse mappings. We prove that, for every ballean (X, E), there exists the unique free vector ...

Іn this article the investigation of groups of fi- nite normal rank is continued. The finiteness of normal rank of nonabelian p-group G is proved where G has a normal elementary abelian p-subgroup A for which quotient ...

We investigate groups in which maximal sub- groups of even order are primary or biprimary. We also research soluble groups with restriction on a number of prime devisors of some proper subgroup orders. We give ...

A 2-monomial matrix over a commutative ring R is by definition any matrix of the form M(t, k, n) = Φ Ik 0 0 tIn−k , 0 < k < n, where t is a non-invertible element of R, Φ the companion matrix to λ n − 1 and Ik ...

The paper is a generalization of . For a group H = hA|Oi, conditions for the equality N1 ∩ N2 = [ N1, N2] are given in terms of pictures, where ¯Ni is the normal closure of a set Ri ⊂ H for i = 1, 2.