The centralisers tag has no wiki summary.

**3**

votes

**1**answer

200 views

### A question on conjugacy classes of central involutions in a finite group

An involution $a$ of a group $G$ is called central if there exists a sylow $2$-subgroup $H$ of $G$ such that $a \in C_G(H)$, or equivalently if the centralizer of $a$ contains a sylow $2$-subgroup.
...

**3**

votes

**1**answer

224 views

### Involution centralizers in simple groups

I often see lower bounds on the size of centralizers of involutions
in finite (nonabelian) simple groups, but is there a general upper bound
for the size of an involution centralizer in such a ...

**6**

votes

**1**answer

309 views

### Centralizers of elements in general linear group over Z mod prime power

I would like to know for which elements $x$ in $G:=Gl_n(\mathbb{Z}/\ell^e\mathbb{Z})$ their centralizers $C_G(x):=\{ y \in G \mid xy=yx\}$ are abelian groups.
Here, $n$ is an integer $\geq 2$ ...

**0**

votes

**0**answers

102 views

### Centralizers of elementary abelian subgroups of $p$-groups

Let $P$ be a $p$-group. It is known that if $E$ is a maximal elementary abelian subgroup of rank 2 in $P$, then $C_P(E)/E$ is cyclic where $C_P(E)$ denotes the centralizer of $E$ in $P$.
This is ...

**5**

votes

**2**answers

493 views

### Lie algebras and non-smoothness of centralisers in bad characteristic

Let $G$ be a simple algebraic group over an algebraically closed
field $k$ of characteristic $p>0$. For $x\in G$, let $C_{G}(x)$
denote the centraliser, considered as a group scheme over $k$. If
...