Questions tagged [character-theory]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
17 votes
1 answer
757 views

Number of solutions to equations in finite groups

Suppose $G$ is a finite group and that $E$ is an equation of the form $x_1 x_2 ... x_n = e$, where each $x_i$ is in the set of symbols $\{x, y, x^{-1}, y^{-1}\}$. Is it always true that the number ...
Paul Boddington's user avatar
53 votes
5 answers
5k views

How much of the ATLAS of finite groups is independently checked and/or computer verified?

In a recent talk Finite groups, yesterday and today Serre made some comments about proofs that rely on the classification of finite simple groups (CFSG) and on the ATLAS of Finite Groups. Namely, he ...
David Roberts's user avatar
  • 33.8k
7 votes
2 answers
735 views

Proofs of a character identity?

Let $G$ be a finite group, $g \geq 0, k\geq 1 $ integers, and $(C_1,...,C_k)$ a tuple of conjugacy classes of $G$. I am interested in proofs of the following identity $$ \sum_{(c_1,...,c_k) \in C_1 \...
user101010's user avatar
  • 5,319