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We prove that all subgroups of cyclic groups are themselves cyclic. We will need Euclid's division algorithm/Euclid's division lemma for this proof. We take an arbitrary subgroup H from our Cyclic group G, then we take an arbitrary element a^t from H. Certainly, all powers of a^t are in H, since H is closed. Then, it only remains to prove that all elements of H are in fact powers of a^t. #AbstractAlgebra
Lesson on Cyclic Groups, Generators, and Cyclic Subgroups: • Cyclic Groups, Generat...
Abstract Algebra Course: • Abstract Algebra
Abstract Algebra Exercises:
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