# Tag Info

### On permanents and determinants of finite groups

I won't discuss the permanent part of the question, but I think the other part can be done easily, even without Galois theory. Let $X = X(G)$ denote the character table of $G$ (rows indexed by complex ...
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### The character table of the symmetric group modulo m

This is true when $m$ is prime and false in general. Counterexample. Take $S_8$ with $m=6$. Computer calculations show that the $\mathbb{Z}$-rank of the character table of $S_8$ with entries taken ...
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### The character table of the symmetric group modulo m

When $m$ is prime there is a simpler proof. The Smith normal form of the character table of $S_n$ is computed at Problem 14 here (solution here). From this it follows that the rank of the character ...
Accepted

### Explicit version of the Burgess theorem

There are now at least two instances of such an explicit result. Theorem 1.1 of Bordignon: https://arxiv.org/abs/2001.05114. Theorem 1.1 (and Corollary 1.2) of Jain-Sharma, Khale, and Liu: https://...
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### What did Frobenius prove about $M_{12}$?

It seems to me that Frobenius is using lots of specific facts about the permutation group $M_{12}$ (and $M_{24}$, respectively) here, and that he has no doubts about the existence of these groups. In ...
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### Tannakian Formalism for the Quaternions and Dihedral Group

Let $V_D$ and $V_Q$ be the two dimensional simple representations of $D_4$ and $Q_8$ respectively. Let $1_D$ and $1_Q$ denote their trivial representations. Suppose that there is a tensor equivalence ...
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### What did Frobenius prove about $M_{12}$?

This summary of Frobenius' 1904 paper might be of use: Thomas Hawkins, The Mathematics of Frobenius in Context (page 527-528).
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Accepted

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