How can we decide how a group is decomposed as a direct sum of cyclic $p$-groups from the character table? Assume the group is finite abelian and that we know the complex character table.
Determining the group decomposition as a direct sum of cyclic p-groups from the character table
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group-theory
representation-theory
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0You should digest the answer to your previous question first. Then you wouldn't need to ask this one. – 2012-06-19
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0The rows of the character table of a finite abelian group $G$ are elements of the group $(\mathbb{C}^\times)^{|G|}$. They form a group under multiplication. That group is isomorphic to $G$. – 2012-06-19