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Results tagged with rt.representation-theory
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user 19075
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
11
votes
Groups in which all characters are rational.
Sylow $2$-subgroups of the symmetric group $S_n$ of degree $n$ are rational.
There was a longstanding conjecture on rational groups saying that Sylow $2$-subgroups of a rational group are also ration …
- 3,738
14
votes
3
answers
1k
views
Does the Alternating group of degree $n>7$ have exactly one irreducible character of degree ...
We know that the alternating group of degree $n>7$ has an irreducible character of degree $n-1$. The latter number is the smallest nontrivial one for each the alternating group has an irreducible char …
- 3,738
2
votes
Bound on the order of a finite group generated by elements $a$ and $b$ of order 2 and $n \ge...
If you are looking for a more abstract proof based on representation and group theory, I suggest you to work on a more general question as follows:
Assume that $G=\langle S\rangle$ is a finite grou …
- 3,738