In this paper, we established the connection between generalized quaternion algebra and real (complex) matrix algebras by using Hamilton operators. We obtained complex matrices corresponding to basis of quaternions. Also, investigated features matrices. get Pauli Then, have shown that produced these is isomorphic Clifford Cl(E_αβ^3) space E_αβ^3.
 Finally, studied relations among symplecti...

Suppose that a group G acts transitively on the points of P, a finite non-Desarguesian projective plane. We prove first that the Sylow 2subgroups of G are cyclic or generalized quaternion; we then prove that if G is insoluble then G/O(G) is isomorphic to SL2(5) or SL2(5).2. MSC(2000): 20B25, 51A35.

Bentea and Tu{a}rnu{a}uceanu~(An. c{S}tiinc{t}. Univ. Al. I.Cuza Iac{s}, Ser. Nouv{a}, Mat., {bf 54(1)} (2008), 209-220)proposed the following problem: Find an explicit formula for thenumber of fuzzy subgroups of a finite hamiltonian group of type$Q_8times mathbb{Z}_n$ where $Q_8$ is the quaternion group oforder $8$ and $n$ is an arbitrary odd integer. In this paper weconsider more general grou...

The study of perfect state transfer on graphs has attracted a great deal attention during the past ten years because its applications to quantum information processing and computation. Perfect is understood be rare phenomenon. This paper establishes necessary sufficient conditions for bi-Cayley graph having over any given finite abelian group. As corollaries, many known new results are obtained...

We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex quaternion matrices, and so on. AMS Mathematics Subject Classification: 15A06; 15A24; 15A33