For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...

The direct product of two Fibonacci tilings can be described as a genuine stone inflation rule with four prototiles. This admits various modifications, which lead to 48 different rules, known the variations. They all result in that are measure-theoretically isomorphic by Halmos–von Neumann theorem. cut and project sets characteristic windows two-dimensional Euclidean internal space. Here, we an...

The purpose of this study is to construct the concept direct product bitonic algebras, and investigate some respective features. Also, commutative homomorphism are studied. Then notion algebras expanded finite family their qualifications practised.

We propose a generalization of the external direct product concept to polyadic algebraic structures which introduces novel properties in two ways: arity can differ from that constituents, and elements different multipliers be \textquotedblleft entangled\textquotedblright\ such is no longer componentwise. The main property we want preserve associativity, gained by using associativity quiver tech...

The properties and applications of kronecker product in quantum theory is studied thoroughly. The use of kronecker product in quantum information theory to get the exact spin Hamiltonian is given. The proof of non-commutativity of matrices, when kronecker product is used between them is given. It is shown that the non-commutative matrices after kronecker product are similar or they are similar ...

By Frucht’s Theorem, every abstract finite group is isomorphic to the automorphism group of some graph. In 1975, Babai characterized which of these abstract groups can be realized as automorphism groups of planar graphs. In this paper, we give a more detailed description of these groups in two steps. First, we describe stabilizers of vertices in connected planar graphs as the class of groups cl...

The quaternion group Q8 is one of the two non-abelian groups of size 8 (up to isomorphism). The other one, D4, can be constructed as a semi-direct product: D4 ∼= Aff(Z/(4)) ∼= Z/(4) o (Z/(4))× ∼= Z/(4) o Z/(2), where the elements of Z/(2) act on Z/(4) as the identity and negation. While Q8 is not a semi-direct product, it can be constructed as the quotient group of a semi-direct product. We wil...