Melvin L. Ott

Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

First Advisor

E. E. Underwood


The purpose of this paper will be to pre sent detailed proofs to selected theorems and to give solutions to various exercises. The proofs for some theorems not directly related to topics under discussion will be omitted and will be denoted with letters rather than being numbered.

The first portion of the paper discusses transformations and subgroups. However, many basic definitions and theorems will not be stated for example definition of a group, subgroup, normal sub­group, factor group, etc. Topics to be emphasized include centralizer, center, and normalizer of a group, characteristic subgroups, con­jugacy and commutator.

In the second part of the paper direct sums are discussed with the ultimate proof of the famous Remak-Krull-Schmidt Theorem.