All Questions

$\DeclareMathOperator\SU{SU}\DeclareMathOperator\Sp{Sp}\DeclareMathOperator\SO{SO}$Let $G$ be a compact connected Lie group. Definition: Two finite subgroups $H_1,H_2$ of $G$ are said to be almost ...

The symplectic group $\mathrm{Sp}_n(q)$ acts on $\mathrm{GL}_{2n}(q)$ by conjugation. All the literature I have found concerning the orbits of action of this kind is "Unipotent conjugacy classes in ...

How can we characterize the finite groups generated by a subset of a single conjugacy class? This post asks for well-known families of finitely generated groups generated by a single conjugacy class. ...

Let $G$ be a finite group and $C$ be a conjugacy class of $G$. It is clear that there exists $k\in \mathbb{N}$, such that $1\cup C\cup C^2 \cup \cdots \cup C^k=\langle C \rangle$. Note that $\langle C ...

$\DeclareMathOperator\Hom{Hom}\DeclareMathOperator\GL{GL}\DeclareMathOperator\Aut{Aut}$Let $f\in \Hom((\Bbb Z/p^2\Bbb Z),\GL_{n}(\Bbb Z / p\Bbb Z))$ be an injective homomorphism. What is the number ...

This is more a request to find out if there is any work in the literature discussing certain things. Is there a naturally defined partial ordering on the set of conjugacy classes of a finite group G? ...