Date of Graduation
Master of Science in Mathematics
group, isomorphic, non-isomorphic, abelian groups, direct product, semidirect product, order
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.
© Haya Ibrahim Binjedaen
Binjedaen, Haya Ibrahim, "When There Is A Unique Group Of A Given Order And Related Results" (2016). MSU Graduate Theses. 2952.