The construction of a class of associative composition algebras qn on R 4 generalizing the wellknown quaternions Q provides an explicit representation of the universal enveloping algebra of the real three-dimensional Lie algebras having tracefree adjoint representations (class A Bianchi type Lie algebras). The identity components of the four-dimensional Lie groups GL(qn,l) Cqn (general linear g...

A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...

a non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized fibonacci sequence , , , . a remarkable application of this definition may be find on the study of random covers in the cryptography. the 2-step generalized sequences for the dihedral groups studied for their pe...

We consider abelian varieties with a group of automorphisms isomorphic to generalized quaternion group. provide isogeny decompositions, compute dimensions the corresponding factors and give conditions under which this decomposition is nontrivial. then specialize our results Jacobians relate them so-called genus-zero actions on Riemann surfaces. A complete classification uniparametric families s...

The punctured power graph P (G) of a finite group G is the graph which has as vertex set the nonidentity elements of G, where two distinct elements are adjacent if one is a power of the other. We show that P (G) has diameter at most 2 if and only if G is nilpotent and every Sylow subgroup of G is either a cyclic group or a generalized quaternion 2-group. Also, we show that if G is a finite grou...

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

in this paper, we introduce and study the notion of precompacttopological generalized groups and some new results are given.

In terms of generators and defining relations, a description is given of the Hochschild cohomology algebra for one of the series of local algebras of quaternion type. As a corollary, the Hochschild cohomology algebra is described for the group algebras of generalized quaternion groups over algebraically closed fields of characteristic 2. Introduction Let R be a finite-dimensional algebra over a...