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Sonja Willis (now Sonja Wieck)
ABSTRACT
Ms. Willis uses procedures she has written in Maple to investigate the
Cayley Digraphs of groups. Her work was inspired by a section in the textbook
"Contemporary Abstract Algebra" by Joseph Gallian. She developed a program
to find Hamiltonian Paths in a group; she extended the Maple "draw" program
to appropriately display Cayley digraphs; and she conducted a study of
Hamiltonian paths for all groups of orders 1-32 (using Groups32 to import
the data to Maple). She has supplied computer proofs of some of the assertions
found in the literature. A Maple worksheet will appear for those
who want to run her procedures.
Evelyn Manalo
ABSTRACT
Ms. Manalo investigates efficient ways to determine whether or not two
groups are isomorphic. Her goal is to find easily computed properties of
groups of low order which can be used to distinguish them. In this thesis
she develops an algorithm which, for an abelian group, produces the canonical
decomposition of a group as a product of cyclic subgroups of prime power
order given the number of elements of various orders. This thesis contains
the algorithm with examples and the necessary support theorems. Groups32
was used to examine examples. The Powerpoint version of her talk,
a downloadable copy of Groups32, and some supplementary programs for Groups32
used in this work will appear.
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