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Let $f$ be a homomorphism from $G$ to $G'$.

1) If order of a subgroup of $H$ of $G$ is $n$, then order of $f(H)$ divides $n$?

2) If the order of Kernel $f$ = $n$, then $f$ is a $n\times 1$ mapping from $G$ onto $f(G)$.

Please suggest how to proceed. Any feedback would be appreciated.

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    I've converted the math in your post to LaTeX. Apologies if I changed your intended meaning in any way.2011-08-17
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    I know that $G'$ is a common symbol for "some other group different from $G$". Unfortunately, it is also a common symbol for the commutator subgroup of $G$. I would suggest using some different symbol.2011-08-17
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    Would you mind changing the title to something more descriptive?2011-08-17

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