Existence of Cyclic Group of Order n
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Theorem
Let $n \in \Z_{>0}$.
Then there exists a cyclic group of order $n$ which is unique up to isomorphism.
Proof
Existence follows from Integers Modulo m under Addition form Cyclic Group.
Uniqueness follows from Cyclic Groups of Same Order are Isomorphic.
$\blacksquare$
Sources
- 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 1.7$: Theorem $7$