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8 votes
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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 ...
Geoff Robinson's user avatar
9 votes
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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 ...
LSpice's user avatar
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5 votes
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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 ...
David White's user avatar
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2 votes
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Are isomorphic maximal tori stably conjugate?

$\DeclareMathOperator\GL{GL}\DeclareMathOperator\SL{SL}\DeclareMathOperator\PGL{PGL}\DeclareMathOperator\Gal{Gal}$Let $(B, S)$ be a Borel–torus pair in $G \mathrel{:=} \mathsf G_2$, let $\alpha_1$ be ...
LSpice's user avatar
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