Special polycyclic generating sequences for finite soluble groups

Generating Sequences of Finite Groups

The Jacobsthal Sequences in Finite Groups

Abstract In this paper, we study the generalized order- Jacobsthal sequences modulo for and the generalized order-k Jacobsthal-Padovan sequence modulo for . Also, we define the generalized order-k Jacobsthal orbit of a k-generator group for and the generalized order-k Jacobsthal-Padovan orbit a k-generator group for . Furthermore, we obtain the lengths of the periods of the generalized order-3 ...

Algorithms for Polycyclic-by-finite Groups Algorithms for Polycyclic-by-finite Groups Table of Contents

OF THE DISSERTATION Algorithms for Polycyclic-by-Finite Groups by Gretchen Ostheimer Dissertation Director: Professor Charles C. Sims Let R be a number eld. We present several algorithms for working with polycyclicbynite subgroups of GL(n;R). Let G be a subgroup of GL(n;R) given by a nite generating set of matrices. We describe an algorithm for deciding whether or not G is polycyclic-bynite. Fo...

Efficient multiplication algorithms for finite polycyclic groups

Let G be a finite soluble group given by a reduced confluent polycyclic presentation. Represent group elements by reduced words. Then there exists an algorithm for multiplying two group elements which has subexponential running time and requires polynomial space. Moreover, given the prime factorisation of the group order, the problem of multiplying two group elements is probabilistically polyno...

Algorithms for polycyclic-by-finite matrix groups

Let K be a number eld. We present several algorithms for working with polycyclic-by-nite subgroups of GL(n; K). Let G be a subgroup of GL(n; K) given by a nite generatingset of matrices. We describe an algorithm for deciding whether or not G is polycyclic-by-nite. For polycyclic-by-nite G, we describe an algorithm for deciding whether or not a given matrix is an element of G. We also describe a...