0
$\begingroup$

It appears to be standard that the set of non-identity involutions in $SL(2, 2^n) = PSL(2, 2^n)$ forms a single conjugacy class. What is the best reference for this?

I note that https://math.stackexchange.com/questions/208255/conjugacy-classes-of-elements-of-a-prime-order-in-psl-2q asked a related question and seems to contain a proof, but is there a published proof?

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ There are many published proofs. This was first done by Dickson, you can see his 1901 book "Linear Groups". More recent expositions include Suzuki's book "Group Theory I" (section III.6) and Gorenstein's "Finite Groups" (section 2.8). $\endgroup$
    – Michael Zieve
    Commented May 15, 2014 at 1:00
  • $\begingroup$ -1 Sorry, but mathoverflow is thought for research level questions. Please ask this kind of question at math.stackexchange.com $\endgroup$
    – j.p.
    Commented May 15, 2014 at 11:31

1 Answer 1

Reset to default
1
$\begingroup$

The comment above gives a few references. The most straightforward proof of this specific question seems to be Lemma (6.3) in "Group Theory I" by Suzuki.

Improve this answer
$\endgroup$
1
  • $\begingroup$ Yes, it is easy to see directly. Setting $q = 2^{n},$ the normalizer of a Sylow $2$-subgroup has order $q(q-1),$ and contains a cyclic subgroup of order $q-1$ which permutes the non-identity elements of the Sylow $2$-subgroup transitively under conjugation. $\endgroup$
    – Geoff Robinson
    Commented May 15, 2014 at 7:20

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .