Given that G is an abelian group and $\Psi: G\to G$ is a homomorphism, what can be said about the kernel of $\Psi$ if $G$ has odd order?
How does an odd order group affect the kernel?
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group-theory
finite-groups
abelian-groups
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1I don't think there can be said anything interesting in this generality, except that the kernel has also odd order :) On the other hand finite abelian groups are classified as sums of various $Z/p^n Z$ so one can explicitly write down a list of all possible kernels. – 2011-12-02