Coset enumeration, based on the methods described by Todd & 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 presentation. We show that it is much easier than it rst appears, albeit at the ...

Freiman’s theorem asserts, roughly speaking, if that a finite set in a torsion-free abelian group has small doubling, then it can be efficiently contained in (or controlled by) a generalised arithmetic progression. This was generalised by Green and Ruzsa to arbitrary abelian groups, where the controlling object is now a coset progression. We extend these results further to solvable groups of bo...

and the Monster simple group was discussed. In this paper, we will provide the technical details. We will determine the structure of the coset subalgebras and show that they are all generated by two conformal vectors of central charge 1/2.We also study the representation theory of these coset subalgebras and show that the product of two Miyamoto involutions is in the desired conjugacy class of ...

This article presents the examination of the possibility that group Eg' F21 operates on a symmetric design with parameters (133,33,8) as its automorphism group. The method based on coset enumeration in group is used.

We construct smallest known trivalent graphs for girths 16 and 18. One construction uses voltage graphs, and the other coset enumeration techniques for group presentations. AMS Subject Classifications: 05C25, 05C35

After explicitly constructing the symmetric space sigma model lagrangian in terms of the coset scalars of the solvable Lie algebra gauge in the current formalism we derive the field equations of the theory.

This paper is a continuation of [33] at which several coset subalgebras of the lattice VOA V2E8 were constructed and the relationship between such algebras with the famous McKay observation on the extended E8 diagram and the Monster simple group were discussed. In this article, we shall provide the technical details. We completely determine the structure of the coset subalgebras constructed and...

Let G be any abelian group and {asGs}ks=1 be a finite system of cosets of subgroups G1, . . . , Gk. We show that if {asGs} k s=1 covers all the elements of G at least m times with the coset atGt irredundant then [G : Gt] 6 2 and furthermore k > m + f([G : Gt]), where f( ∏ r i=1 p αi i ) = ∑ r i=1 αi(pi − 1) if p1, . . . , pr are distinct primes and α1, . . . , αr are nonnegative integers. This ...

The SW(3/2, 3/2, 2) superconformal algebra is a W algebra with two free parameters. It consists of 3 superconformal currents of spins 3/2, 3/2 and 2. The algebra is proved to be the symmetry algebra of the coset su(2)⊕su(2)⊕su(2) su(2) . At the central charge c = 10 2 the algebra coincides with the superconformal algebra associated to manifolds of G2 holonomy. The unitary minimal models of the ...