The purpose of this paper is to provide an introduction to some computational techniques which have proved useful in the study of large permutation groups. In particular they have been used to study… (More)

Let G be a finite group which possesses a chain of characteristic subgroups with quotients of moderate size. This paper describes methods for computing the order of and for deciding membership in a… (More)

Computational group theory has a history going back more than 80 years. It is a collaborative e ort of researchers in a wide range of areas in both mathematics and computer science. The eld has… (More)

The following problem is frequently encountered while computing with groups: Given a set X of permutations on a finite set ~, determine the order of the group G generated by X. Usually we are also… (More)

Coset enumeration is a procedure for verifying that a subgroup of a finitely presented group has finite index. The procedure was first described in Todd & Coxeter (1936). A survey of coset… (More)

To examine computationally the growth rate of a group with respect to a set of generators, one needs to be able to multiply elements of the group very quickly and to store large sets of group… (More)

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… (More)