Enumeration of Metacyclicp-Groups

Enumeration of Schur Rings Over Small Groups

Coset enumeration of groups generated by symmetric sets of involutions

The well-known Todd-Coxeter algorithm [14], which may be viewed as a means of constructing permutation representations of finitely presented groups, remains a primary reference for coset enumeration programs. All the strategies and variants of this algorithm perform essentially the same calculations as the original algorithm, merely choosing different orders in which to process the available in...

The Enumeration of Fully Commutative Elements of Coxeter Groups

A Coxeter group element w is fully commutative if any reduced expression for w can be obtained from any other via the interchange of commuting generators. For example, in the symmetric group of degree n, the number of fully commutative elements is the nth Catalan number. The Coxeter groups with finitely many fully commutative elements can be arranged into seven infinite families An , Bn , Dn , ...

Combinatorial method in the coset enumeration of symmetrically generated groups

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

Zeta functions of groups and enumeration in Bruhat-Tits buildings

We introduce a new method to calculate local normal zeta functions of finitely generated, torsion-free nilpotent groups, T-groups in short. It is based on an enumeration of vertices in the Bruhat-Tits building for Sln(Qp). It enables us to give explicit computations for T-groups of class 2 with small centres and to derive local functional equations. Examples include formulae for non-uniform nor...