Timeline for Is the Singer cycle preserved by field automorphisms and graph automorphisms?

9 events

when toggle format	what		by	license	comment
May 25, 2020 at 9:13	vote	accept	Groups
May 25, 2020 at 8:54	answer	added	Derek Holt		timeline score: 1
May 25, 2020 at 8:27	comment	added	Groups		@DerekHolt I can now see that a field automorphism normalises $\langle x\rangle$ by Anton's comment. But how about the graph automorphism (even though the answer seems to be yes)?
May 25, 2020 at 7:44	comment	added	Derek Holt		So the answer to the question is yes, this maximal subgroup extends to a maximal subgroup of ${\rm Aut}(T)$.
May 25, 2020 at 6:32	history	edited	Groups	CC BY-SA 4.0	deleted 3 characters in body
May 25, 2020 at 6:07	comment	added	Anton B		For other questions see "The subgroup Structure of the Finite Classical Group" by P. Kleidman and M. Liebeck, it looks like $\S 4.3$ has some answers. Equation (4.3.8) shows that there is a field automorphism of $T$ normalising $\langle x \rangle$.
May 25, 2020 at 6:01	comment	added	Anton B		There is no uniform shape for $x$. But there is the way to construct it in a particular situation (for given $n$ and $q$), see M. W. Short, "The primitive soluble permutation groups of degree less than 256," page 15. But it is going to be the matrix in not the same basis in which the matrix of $\sigma$ is a permutational matrix most probably.
May 22, 2020 at 5:49	history	edited	Groups	CC BY-SA 4.0	edited title
May 22, 2020 at 5:35	history	asked	Groups	CC BY-SA 4.0