We describe the couplings of six-dimensional supergravity, which contain a self-dual tensor multiplet, to n T anti-self-dual tensor matter multiplets, n V vector multiplets and n H hypermultiplets. The scalar fields of the tensor multiplets form a coset SO(nT , 1)/SO(nT ), while the scalars in the hypermultiplets form quaternionic Kähler symmetric spaces, the generic example being Sp(nH , 1)/Sp...

Let a finite presentation be given for an associative, in general non-commulative algebra E, with identity, over a field. We study an algorithm for the construction, from this presentation, of linear, i.e, matrix, representations of this algebra. A set of vector constraints which is given as part of the initial data determines which particular representation of E is produced. This construction ...

A brief overview of strings propagating on noncompact coset spaces G/H is presented in terms of gauged WZW models. The role played by isometries in the existence of target space duality and by fixed points of the gauged transformations in the existence of singularities and horizons, is emphasized. A general classification of the spaces with a single time-like coordinate is presented. The spacet...

‎there is much interest in finding short presentations for the finite‎ ‎simple groups‎. ‎indeed it has been suggested that all these groups are‎ ‎efficient in a technical sense‎. ‎in previous papers we produced nice‎ ‎efficient presentations for all except one of the simple groups with‎ ‎order less than one million‎. ‎here we show that all simple groups with‎ ‎order between $1$ million and $5$ ...

Julius Whiston showed that the size of an independent generating set in the symmetric group Sn is at most n−1. We determine all sets meeting this bound. We also give some general remarks on the maximum size of an independent generating set of a group and its relationship to coset geometries for the group. In particular, we determine all coset geometries of maximum rank for the symmetric group S...

Coset enumeration, based on the methods described by Todd and Coxeter, is one of the basic tools for investigating nitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. Here we consider one such family of presentations proposed by B.H. Neumann. We show that the problems ar...

Coset enumeration, based on the methods described by Todd and Coxeter, is one of the most important tools for investigating nitely presented groups. Such methods do not, in general, constitute an algorithm. Each problem has to be addressed individually, and determining whether or not an acceptable solution for a diicult problem can be found using given resources requires an empirical approach (...

The 14 Killing vectors of the target space for five-dimensional minimal supergravity reduced to three dimensions are explicitly constructed in terms of the original field variables. These vectors generate the Lie algebra of G2. We also construct a symmetrical 7× 7 matrix representative of the coset G2(+2)/((SL(2, R)× SL(2, R)) as a function of the same fields. ∗Email: [email protected] 1

Let H and K be subgroups of a group G. The double cosets of H and K in G are the sets HgK, g E G. In this paper we describe a procedure, P, for determining the cardinality of the set H\G/K of double cosets of H and K in G given a finite presentation for G and finite sets of generators for H and K. It is well known that the problem of determining whether or not a group G defined by a finite pres...

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