3 votes

Why do characters fail to characterize non-abelian LCH-groups?

The short answer is that if $G$ is a group and $A$ an abelian group (like $\mathbb T$), then every group homomorphism $\phi\colon G\to A$ factors through the abelianization $G/[G,G]$. Here $[G,G]$ is ...
MaoWao's user avatar
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1 vote

Every irreducible character of $S_n$ is an integer valued function.

Personally I do not know how to do this without either Galois theory or the construction of the Specht modules. Here is the Galois theory argument, just to record it here. An element $g$ of a finite ...
Qiaochu Yuan's user avatar

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