Quotient group in finite abelian group.

Asked Jun 06 '17 at 06:45

Active Jun 06 '17 at 10:42

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Statement "If G is finite abelian group and H is its subgroup then there is a normal subgroup N of G such that G/N is isomorphic to H ."

Clearly [G:H] divides order of G .As G is abelian therefor there exists a normal subgroup of order [G: H] ( Say N). Now o (G)/o (H)=o (N) . I.e o (G)/o (N) =o (H) but How can I prove above statement?

edited Jun 06 '17 at 10:42

user26857

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asked Jun 06 '17 at 06:45

Gilll

1

Have you seen the structure theorem for finite abelian groups? – Prahlad Vaidyanathan Jun 06 '17 at 06:46
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This is not a trivial result. One way to prove it is to first prove that the character group of $G$ is isomorphic to $G$. – Angina Seng Jun 06 '17 at 06:47

Quotient group in finite abelian group.

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