All Questions
8 questions
2
votes
0
answers
108
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Involution centralizers in $\mathrm{PCSO}^{+}(8,3)$
According to Table 4.5.1 of [1], there should be 10 classes of involutions of type "p" and "e" in $\operatorname{Aut}(K)$ where $K=K_a=P\Omega^{+}(8,3)$.
And Table 4.5.1 also gives ...
- 217
0
votes
0
answers
62
views
Involutions in $\operatorname {PSO}(4,K)$
In the algebraic group $G=\operatorname {PSO}(4,K)$ where $K$ is an algebraically closed field of an odd characteristic, how many different classes of involutions are there and what are the ...
- 217
0
votes
1
answer
102
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An explicit matrix form in the symplectic group
In the algebraic group $G=\operatorname {PCSp}(2^{r},K)$ where $K$ is an algebraically closed field of an odd characteristic, there is a conjugacy class of involutions with representative:
$$
e=\left[...
- 217
0
votes
1
answer
88
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An explicit matrix form
In the algebraic group $G=\operatorname {PCGO}(2m,K)$ where $K$ is an algebraically closed field of an odd characteristic, there is a conjugacy class of involutions with representative:
$$
e=\left[
\...
- 217
1
vote
0
answers
99
views
Almost simple groups and their involutions without CFSG
Suppose $A$ is a finite almost simple group (meaning, by definition, that there exists a finite simple group $P$ such that $P \leq A \leq \mathrm{Aut}(P)$). Suppose furthermore that $A$ acts $2$-...
- 4,547
4
votes
0
answers
186
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On 2-groups of exponent 4 and class 2
Suppose A is a 2-group with the following properties:
$\lvert A \rvert = t^3$ with $t$ some even power of $2$;
$A$ and $Z(A)$ (the center of $A$) are of exponent $4$;
$\lvert Z(A) \rvert = t$ and $[A,...
- 4,547
4
votes
1
answer
698
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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.
...
- 1,197
3
votes
1
answer
746
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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 ...
- 4,547