3
votes
Accepted
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 ...
- 14.7k
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 ...
- 409k
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