## New answers tagged conjugacy-classes

8
votes

Accepted

### Number of conjugacy classes of pairs of commuting elements II

Revised answer, to cover more of question: The proof that $r_{G} \geq \frac{8p}{3}$ if $G$ is non-Abelian is tedious, but not too difficult, I think, and this is attained, (as you say),for $p = 3$ by ...

9
votes

Accepted

### A pair of non-conjugate subgroups: a simple proof

I think that the elements $g = \dfrac1{\sqrt2}\begin{pmatrix} 1 & 1 \\ -1 & 1 \end{pmatrix}^{\oplus3}$ and $h = \dfrac1 2\begin{pmatrix} 1 & 1 & 1 & 0 & 1 & 0 \\ -1 & 1 ...

5
votes

Accepted

### Is there a way to study the relationship between the category of finite groups and their conjugacy classes categorically?

This question will likely be closed, but I'll try to give the OP some references before it is. First, let me answer the OP's question in the comments, regarding why this is vague and why the question ...

2
votes

Accepted

### Are isomorphic maximal tori stably conjugate?

$\DeclareMathOperator\GL{GL}\DeclareMathOperator\SL{SL}\DeclareMathOperator\PGL{PGL}\DeclareMathOperator\Gal{Gal}$Let $(B, S)$ be a Borelâ€“torus pair in $G \mathrel{:=} \mathsf G_2$, let $\alpha_1$ be ...

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