Prior to this paper all small simple groups were known to be efficient but the status of four of their covering groups was unknown. We produce nice efficient presentations for all of these groups, resolving the previously unknown cases. We give presentations that are better than available before in terms of length and in terms of computational properties. In many cases our presentations have mi...

For a finite group G and a non-negative integer s, let P(G,s) be the probability that a randomly chosen s-tuple generates G. Philip Hall gave an explicit formula for P(G,s), exhibiting the latter as a finite Dirichlet series. One can therefore speak of P(G,s) for an arbitrary complex number s. The reciprocal of this function of s is called the zeta function of G. The present work arose from an ...

We compute branching functions of G/H coset models using a BRST invariant branching function formulae, i.e. a branching function that respects a BRST invariance of the model. This ensures that only the coset degrees of freedom will propagate. We consider G/H for rank(G/H) = 0 models which includes the Kazama-Suzuki construction, and Gk1 ×Gk2/Gk1+k2 models. Our calculations here confirm in part ...

The Todd-Coxeter coset enumeration algorithm is one of the most powerful tools of computational group theory. It may be viewed as a means of constructing permutation representations of nitely presented groups. In this paper we present an analogous algorithm for directly constructing matrix representations over many elds. In fact the algorithm is more general than this, and can be used to constr...

In these notes we discuss coset enumeration and basic permutation group algorithms. To illustrate some applications to graphs and nite geometries, we classify and study some graphs which are locally the incidence graph of the 2 ? (11; 5; 2) design.

This paper presents a parametrized design technique for cellular permutation arrays based on coset decompositions of symmetric groups. A new type of permutation cell, referred to as a coset generator, is introduced to customize the propagation delay, fan-in, fan-out, and number of edges in the target network. To aid in the design process, a cost function is derived expressing the number of edge...

Recently, we have studied the general Virasoro construction at one loop in the background of the general non-linear sigma model. Here, we find the action formulation of these new conformal field theories when the background sigma model is itself conformal. In this case, the new conformal field theories are described by a large class of new spin-two gauged sigma models. As examples of the new ac...

Andrews and Curtis have conjectured that every balanced presentation of the trivial group can be transformed into a standard presentation by a finite sequence of elementary transformations. It can be difficult to determine whether or not the conjecture holds for a particular presentation. We show that the utility PEACE, which produces proofs based on Todd-Coxeter coset enumeration, can produce ...

We consider superstring sigma models that are based on coset superspaces G/H in which H arises as the fixed point set of an order-4 automorphism of G. We show by means of twistor theory that the corresponding first-order system, consisting of the Maurer-Cartan equations and the equations of motion, arises from a dimensional reduction of some generalised self-dual Yang-Mills equations in eight d...