Date of Award
Union College Only
Bachelor of Science
group, subgroup, qoutient groups, properties, math
This paper looks at groups which can be written as unions of their proper subgroups in various ways. We will show that a group can be written as a union of three proper subgroups if and only if it has a quotient isomorphic to C2 ´ C2. We will then investigate groups which can be written as n proper subgroups for n ³ 3. This investigation will lead to several questions: When can a group be written as a union n proper normal subgroups? When can a group be written as the union of the conjugates of n proper subgroups? If a group can be written as a union of its proper subgroups, when is the choice of subgroups unique? These questions will be addressed in the paper.
Miles, Benjamin H., "Groups as the union of proper subgroups, normal subgroups, and other structures" (2010). Honors Theses. 1191.