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user 35416
For questions about the algebraic concept of 'character': a function from a group into a field satisfying certain properties. Not to be confused with the more commonly known psychological term.
4
votes
Proving interesting theorems about S_n using its character table.
You need to be able to compute the Frobenius-Schur indicators of the characters, so you need to know how the conjugacy classes multiply. …
- 13k
7
votes
The zero entries in the character table of a finite group
The proof uses the integrality property of central characters that John Murray mentions. …
- 13k
6
votes
Is a finite group given by its character table if its Sylow subgroups are so?
The answer to the first question is negative. The group ${\rm SL}_2(\mathbb{F}_3)$ has a $2$-Sylow subgroup isomorphic to $Q_8$, which is not determined by its character table, but ${\rm SL}_2(\mathbb …
- 13k
16
votes
Accepted
Finite groups with integral character table
It follows from two facts: firstly, characters "separate" conjugacy classes, i.e. if two elements are not conjugate, then there exists an irreducible character that takes different values on them; and …
- 13k