In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitational interactions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basis and are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamental interactions of Nature. email address: [email protected]...

If W is an infinite rank 3 Coxeter group, whose Coxeter diagram has no infinite bonds, then the automorphism group of W is generated by the inner automorphisms and any automorphisms induced from automorphisms of the Coxeter diagram. Indeed Aut(W ) is the semi-direct product of Inn(W ) and the group of graph automorphisms.

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

We give an algorithm for enumerating cosets of a group defined as a finite homomorphic image of a semi-direct product of free products of cyclic groups by a group of monomial automorphisms. Lots of finite groups, including some of the sporadic simple groups can be defined in this mannar. Mathematics Subject Classification: 20Bxx

Strictly positive definite functions are used as basis functions for approximation methods in various contexts. Using a group theoretic interpretation of Bochner’s Theorem we give a sufficient condition for strictly positive definite functions on a semi-direct product which are invariant under the natural action of a given subgroup. As an application strictly positive definite, reflection invar...

The microwave spectrum of 2,5-dimethylthiophene, a sulfur-containing five-membered ring with two conjugated double bonds, was recorded in the frequency range from 2 to 40 GHz using molecular beam Fourier transform technique. Highly accurate molecular parameters were determined. A labeling scheme for the group G36 written as the semi-direct product (C(I)(3) × C(I)(3)) ⋊ C(2v) was introduced.

We describe a class of non-central extensions of the diffeomorphism algebra in N -dimensional spacetime, and construct lowest-energy modules thereof, thus generalizing work of Eswara-Rao and Moody. There is one representation for each representation of V ir⋉̃k0 ĝl(N) (an extension of the semi-direct product). Similar modules are constructed for gauge algebras.

We provide the set of left-invariant minimal unit vector fields on the semi-direct product Rn oP R, where P is a nonsingular diagonal matrix and on the 7 classes of 4-dimensional solvable Lie groups of the form R3 oP R which are unimodular and of type (R).

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...

Let G1 × G2 be a subgroup of SO3(R) such that the two factors G1 and G2 are non-trivial groups. We show that if G1 × G2 is not abelian, then one factor is the (abelian) group of order 2, and the other factor is nonabelian and contains an element of order 2. There exist finite and infinite such non-abelian subgroups. Let F2 be the free group of rank 2. It is well-known that the group SO3(R) has ...