Prove that in a finite cyclic group, each subgroup has size dividing the size of...

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Prove that in a finite cyclic group, each subgroup has size dividing the size of the group. Conversely, given a positive divisor of the size of the group, there is a subgroup of that size.

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Proof Let G hgi with size m Any subgroup has the form hgki for some k The size ofthis subgroup is the order of g k which is mk m by the handout on See Answer

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Prove that in a finite cyclic group, each subgroup has size dividing the size of...

80.2K

Verified Solution

Question

Advance Math

Prove that in a finite cyclic group, each subgroup has size dividing the size of the group. Conversely, given a positive divisor of the size of the group, there is a subgroup of that size.

Answer & Explanation Solved by verified expert

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