Let $H \leq S_n$ be an intransitive group with orbits $\Omega_1, \Omega_2, \ldots ,\Omega_k$. Then certainly $H$ is a subdirect product of the direct its projections on each orbit, $H|_{\Omega_1} \times H|_{\Omega_2} H|_{\Omega_k}$. Here we provide polynomial time algorithm for computing finest partition $P$ $H$-orbits such that = \prod_{c \in P} H|_c$ and demonstrate usefulness in some applica...

The notion of semi-direct product Poisson $G$-spaces is applied to illuminate examples arising in spin-extensions Ruijsenaars models.

In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups Zpr ⋊ Zq, for p and q prime. We first present a classification of these groups in five classes. Then, we describe a polynomial-time quantum algorithm solving the HSP over all the groups of one of these classes: the groups of the form Zpr ⋊ Zp, where p is an odd prime. Our algorithm works ev...

A quantum algorithm for the Hidden Subgroup Problem over the group Z/pZ o Z/qZ is presented. This algorithm, which for certain parameters of the group qualifies as ‘efficient’, generalizes prior work on related semi-direct product groups. 1998 ACM Subject Classification F.1.2 Modes of Computation, F.2.2 Nonnumerical Algorithms and Problems