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Subgroups of Product Groups
Devitt-Ryder, Robin Michael
Interlando, CarmeloHui, StefenRoot, William
Our goal is to count the number of subgroups of the direct product of finite cyclic groups, Zm _ Zn. When m and n are relatively prime, Zm _ Zn is isomorphic to Zmn. Counting the number of subgroups of Zmn is a simple exercise in combinatorics. However, if m and n are not relatively prime, then we use Goursat's (lesser-known) Theorem to find the number of subgroups of Zm _ Zn. We may also extend the usage of this theorem to cases beyond the direct product of finite cyclic groups.
Mathematics and Statistics
Master of Arts (M.A.) San Diego State University, 2014
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