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Results tagged with gr.group-theory
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user 4366
Questions about the branch of algebra that deals with groups.
6
votes
3
answers
1k
views
An application of Maschke's theorem
I've been teaching some elementary representation theory to undergraduates, and want to provide applications of Maschke's theorem to complex group algebras to present in class. In particular, I'd like …
- 1,472
2
votes
What natural numbers can be considered as the product of orders of elements of a finite (abe...
First of all, the Putnam exam problem is about 2-groups and I highly doubt that the generalization proposed above is in any way tractable. That having been said, for $S_n$, every permutation has a cyc …
- 1,472
2
votes
permutation representation of $S_n$
Since you only care about the completely reducible case, I'll assume $K=\mathbb{C}$.
The easiest way that I know of to construct irreducible $S_n$ representations is a special case of the constructio …
- 1,472
1
vote
Accepted
Homomorphisms from irreducible spaces to reducible spaces
I assume you are talking about representations of $S_n$ over $\mathbb{C}$. In this case, $\mathbb{C}S_n$ is left semi-simple by Maschke's Theorem, so every representation of $S_n$ is a direct sum of i …
- 1,472