Date of Graduation

Summer 2016

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Les Reid

Keywords

group, isomorphic, non-isomorphic, abelian groups, direct product, semidirect product, order

Subject Categories

Mathematics

Abstract

It is well-known that any group whose order is a prime number must be cyclic, that is there is only one group of that order up to isomorphism. This is also the case for some non-prime orders, for example there is only one group of order 15 up to isomorphism. This thesis provides the necessary background material to completely characterize those n for which these is a unique group of order n, namely when n and the Euler phi function of n are relatively prime. We also determine for which n there are exactly two groups of order n up to isomorphism.

Copyright

© Haya Ibrahim Binjedaen

Open Access

Included in

Mathematics Commons

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