The de ciency of a nite group presentation P : h X j R i is def(P) = jXj jRj, the di erence between the numbers of generators and de ning relators. For a given nitely presented group G, the de ciencies of nite presentations for G are bounded above (for example by the torsion free rank of the abelianisation G=G). The de ciency of G, def(G), is the maximum of the de ciencies of all nite presentat...

In this paper we introduce new techniques for the eecient computation of a Fourier transform on a nite group. We use the decomposition of a group into double cosets and a graph theoretic indexing scheme to derive algorithms that generalize the Cooley-Tukey FFT to arbitrary nite groups. We apply our general results to special linear groups and low rank symmetric groups, and obtain new eecient al...

In this paper we survey some recent work directed towards generalizing the fast Fourier transform (FFT). We work primarily from the point of view of group representation theory. In this setting the classical FFT can be viewed as a family of e cient algorithms for computing the Fourier transform of either a function de ned on a nite abelian group, or a bandlimited function on a compact abelian g...

In recent years, there has been a lot of interest in the use of discrete-time recurrent neural nets (DTRNN) to learn nite-state tasks, and in the computational power of DTRNN, particularly in connection with nite-state computation. This paper describes a simple strategy to devise stable encodings of sequential nite-state translators (SFST) in a second-order DTRNN with units having bounded, stri...

An explicit character formula is established for any strongly generic nite-dimensional irreducible g-module, g being an arbitrary nite-dimensional complex Lie superalgebra. This character formula had been conjectured earlier by Vera Serganova and the author for any generic irreducible nite-dimensional g-module, i.e. such that its highest weight is far enough from the walls of the Weyl chambers....

The groups (m;n; p; q) = ha; b j a = b = (ab) = [a; b] = 1i were introduced and studied by Brahana [?, ?], Coxeter [?, ?, ?, ?] and Sinkov [?, ?, ?, ?, ?]. This initial work was followed by a later paper of Sinkov [?], and a paper by Leech and Mennicke [?]. More recently, interest in deciding which values of the parameters m;n; p; q yield nite groups and which in nite has been revived by Grove ...

We determine all nite-dimensional simple Lie superalgebras L such that U(L) satisses a primeness criterion due to Bell. Some open problems related to primeness of enveloping algebras are listed. 1. Introduction This paper gives a complete account of the application of a primeness criterion, introduced in Bel90], to the enveloping algebras of the Cartan type nite dimensional simple Lie superalge...

We present a new algorithm that extends the techniques of the Pohlig-Hellman algorithm for discrete logarithm computation to the following situation: Given a nite abelian group and group elements h, g1; : : : ; g l , compute the least positive integer y and numbers x1 ; : : : ; x l such that h y = Q gi x i. This computational problem is important for computing the structure of a nite abelian gr...

in this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional euclidean space, which are the einstein and möbius gyrovector spaces. we introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and see its interest...

In 1979, two constructions for making partitionable graphs were introduced in (by Chv2 atal et al. (Ann. Discrete Math. 21 (1984) 197)). The graphs produced by the second construction are called CGPW graphs. A near-factorization (A; B) of a %nite group is roughly speaking a non-trivial factorization of G minus one element into two subsets A and B. Every CGPW graph with n vertices turns out to b...