In this paper we introduce the notion of the neat range one for Bezout duo-domains. We show that a distributive Bezout domain is an elementary divisor domain if and only if it is a duo-domain of neat range one.

Let G be a finite group. Recall that a subgroup A of G is said to permute with a subgroup B if AB = BA. A subgroup A of G is said to be S-quasinormal or S-permutable in G if A permutes with all Sylow subgroups of G. ...

Let G be a group and p a prime number. G is said to be a Yp-group if whenever K is a p-subgroup of G then every subgroup of K is an S-permutable subgroup in NG(K). The group G is a soluble PST-group if and only if G is ...

We construct a simplified resolution for the trivial G-module Z, where G is a finite abelian group, and compare it with the standard resolution. We use it to calculate cohomologies of irreducible G-lattices and their duals.

Dickson characterized groups in terms of one-sided invertibility. In this note, we give comparable characterizations for Bol and Moufang loops.

We introduce the equivalence relation ρ on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing l-cycles with l > 4 to an equivalent Carter diagram containing only 4-cycles. ...

Let D = hα, βi be a dihedral group generated by the involutions α and β and let F = hαβi. Suppose that D acts on a finite group G by automorphisms in such a way that CG(F) = 1. In the present paper we prove that the ...

The notions of (G, φ)-crossed product and quasicrossed system are introduced in the setting of (G, φ)-quasiassociative algebras, i.e., algebras endowed with a grading by a group G, satisfying a “quasiassociative” law. It ...

We extend the concept of path-cycles, defined in [2], to the semigroup Pn, of all partial maps on Xn = {1, 2, . . . , n}, and show that the classical decomposition of permutations into disjoint cycles can be extended ...

In this paper we study the properties of positive series such that its terms are reciprocals of the elements of Jacobsthal-Lucas sequence (Jn+2 = 2Jn+1 + Jn, J1 = 2, J2 = 1). In particular, we consider the properties of ...