Algebra and Discrete Mathematics, 2005, № 3

A note on c-normal subgroups of finite groups

Sat, 01 Jan 2005 00:00:00 GMT

A note on c-normal subgroups of finite groups Skiba, A.N. Let G be a finite group. We fix in every noncyclic Sylow subgroup P of G some its subgroup D satisfying 1 < |D| < |P| and study the structure of G under assumption that all subgroups H of P with |H| = |D| are c-normal in G.

Ternary Hopf algebras

Sat, 01 Jan 2005 00:00:00 GMT

Ternary Hopf algebras Zekovic, B. In this paper we introduce the notion of a ternary Hopf algebra and prove that it can be embedded into a universal enveloping Hopf algebra.

Two-generated graded algebras

Sat, 01 Jan 2005 00:00:00 GMT

Two-generated graded algebras Shirikov, E.N. The paper is devoted to classification of twogenerated graded algebras. We show that under some general assumptions there exist two classes of these algebras, namely quantum polynomials and Jordanian plane. We study prime spectrum, the semigroup of endomorphisms and the Lie algebra of derivations of Jordanian plane.

On square-Hamiltonian graphs

Sat, 01 Jan 2005 00:00:00 GMT

On square-Hamiltonian graphs Protasova, K.D. A finite connected graph G is called squareHamiltonian if G² is Hamiltonian. We prove that any join of the family of Hamiltonian graphs by tree is square-Hamiltonian. Applying this statement we show that the line graph and any round-about reconstruction of an arbitrary finite connected graph is square-Hamiltonian.