A concept of basic matrix semigroups over fields (with some variations) is introduced and throughly investigated. Sections 1 and 2 contain main definitions, Section 3 treats some properties of basic semigroups, Section 4 ...

In this paper the well-known connection between hyperidentities of an algebra and identities satisfied by the clone of this algebra is studied in a restricted setting, that of n-ary full hyperidentities and identities of ...

Let H be a normal subgroup of a finite group G. A number of authors have investigated the structure of G under the assumption that all minimal or maximal subgroups in Sylow subgroups of H are well-situated in G. A general ...

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 ...

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 R i ⊂ H for i = 1, 2.

It is shown that the set of pairwise non-isomorphic 2-generated simple groups of exponent n (n ≥ 248 and n is odd or divisible by 29) is of cardinality continuum. As a corollary, for any sufficiently large n the set of ...

Let denote an extended Dynkin diagram with vertex set 0 = {0, 1, . . . , n}. For a vertex i, denote by S(i) the set of vertices j such that there is an edge joining i and j; one assumes the diagram has a unique vertex ...

In the space of irreducible unitary representations of a linear group over an algebra of type e A2 an open dense subset of representations in the general position is singled out. This set is identified, up to simple ...