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)

Climate change has been implicated as a root cause of the recent surge in natural disturbance events such as storms, wildfires, and insect outbreaks. This climate-based surge has led to a greater… (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)