The semi-direct product of arbitrary two monoids and a presentation for this product have received considerable attention, see for instance [12], [14] and [15]. In [15], Wang defined a trivialiser set of the Squier complex associated with this presentation. In this paper, as a main result, we discuss necessary and sufficient conditions for the standard presentation of the semi-direct product of...

We obtain a kind of structure theorem for the automorphism group AutA of a unital C-algebra A. According to it, AutA can be regarded as a subgroup of the semi-direct product of direct product group consisting of some family of projective unitary groups and some permutation group on the spectrum of A.

recently‎, ‎the authors gave some conditions under which a direct product‎ ‎of finitely many groups is $mathcal{v}-$capable if and only if each of its‎ ‎factors is $mathcal{v}-$capable for some varieties $mathcal{v}$‎. ‎in this paper‎, ‎we extend this fact to any infinite direct product of groups‎. ‎moreover‎, ‎we conclude some results for $mathcal{v}-$capability of direct products of infinitel...

A five term sequence for the low degree cohomology of a smash product of (cocommutative) Hopf algebras is obtained, generalizing that of Tahara for a semi-direct product of groups

We consider the standard semi-direct product AoB of finite groups A,B. We show that with certain choices of generators for these three groups, the Cayley graph of A o B is (essentially) the zigzag product of the Cayley graphs of A and B. Thus, using the results of [RVW00], the new Cayley graph is an expander if and only if its two components are. We develop some general ways of using this const...

In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups Zn ⋊ Zq. The definition of the semi-direct product depending on the choice of an homomorphism, we first analyze the different possibilities for this homomorphism in function of n and q. Then, we present a polynomial-time quantum algorithm solving the HSP over the groups of the form Zpr ⋊ Zp...