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Mathematics
Linear and Abstract Algebra
List all the subgroups H of C_(12)
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[QUOTE="Euge, post: 6776713, member: 705178"] Every subgroup of a cyclic group is cyclic, and for every positive divisor $d$ of $n$, there is a unique subgroup of $\Bbb Z_n$ of order $d$. The positive divisors of $12$ are $1, 2, 3, 4, 6$, and $12$. Thus, the subgroups of $\Bbb Z_{12}$ are $k \Bbb Z_{12}$ where $k = 1, 2, 3, 4, 6, 12$. By the correspondence the subgroups of $C_{12}$ are $\omega^k C_{12}$ for the same $k$-values. [/QUOTE]
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Linear and Abstract Algebra
List all the subgroups H of C_(12)
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