A Polycyclic Quotient Algorithm

A hybrid quotient algorithm

We describe an algorithm which takes as input a finitely presented group F, a finite confluent rewriting system for a quotient G and a prime p, and returns as output a finite confluent rewriting system for the largest extension of an elementary abelian group in characteristic p by G which is still an epimorphic image of F.

A nilpotent quotient algorithm for L-presented groups

The main part of this paper contains a description of a nilpotent quotient algorithm for L-presented groups and a report on applications of its implementation in the computer algebra system GAP. The appendix introduces two new infinite series of L-presented groups. Apart from being of interest in their own right, these new L-presented groups serve as examples for applications of the nilpotent q...

Variable step-size LMS algorithm with a quotient form

An improved robust variable step-size least mean square (LMS) algorithm is developed in this paper. Unlike many existing approaches, we adjust the variable step-size using a quotient form of filtered versions of the quadratic error. The filtered estimates of the error are based on exponential windows, applying different decaying factors for the estimations in the numerator and denominator. The ...

A Nilpotent Quotient Algorithm for Graded Lie Rings

A nilpotent quotient algorithm for graded Lie rings of prime characteristic is described. The algorithm has been implemented and applications have been made to the investigation of the associated Lie rings of Burnside groups. New results about Lie rings and Burnside groups are presented. These include detailed information on groups of exponent 5 and 7 and their associated Lie rings. Appeared: J...

A Note on Strongly Quotient Graphs