Journal of Lie Theory

no. 1
θ-Semisimple Classes of Type D in PSLn(q)
Journal of Lie Theory, Volume 26 (2016) no. 1, pp. 193-218
\def\F{{\Bbb F}} \def\N{{\Bbb N}} Let $p$ be an odd prime, $m\in \N$ and set $q=p^m$, $G={\rm PSL}_n(q)$. Let $\theta$ be a standard graph automorphism of $G$, $d$ be a diagonal automorphism and ${\rm Fr}_q$ be the Frobenius endomorphism of ${\rm PSL}_n(\overline{\F_q})$. We show that every $(d\circ \theta)$-conjugacy class of a $(d\circ \theta,p)$-regular element in $G$ is represented in some ${\rm Fr}_q$-stable maximal torus of ${\rm PSL}_n(\overline{\F_q})$ and that most of them are of type D. We write out the possible exceptions and show that, in particular, if $n\geq 5$ is either odd or a multiple of $4$ and $q>7$, then all such classes are of type D. We develop general arguments to deal with twisted classes in finite groups.
DOI: 10.5802/jolt.887
Classification: 16W30
Keywords: Hopf algebras, twisted conjugacy classes, finite simple groups 
@article{JOLT_2016_26_1_a9,
     author = {G. Carnovale and A. Garc{\'\i}a Iglesias},
     title = {\ensuremath{\theta}-Semisimple {Classes} of {Type} {D} in {PSL\protect\textsubscript{n}(q)}},
     journal = {Journal of Lie Theory},
     pages = {193--218},
     year = {2016},
     volume = {26},
     number = {1},
     doi = {10.5802/jolt.887},
     zbl = {1372.20046},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.887/}
}
TY  - JOUR
AU  - G. Carnovale
AU  - A. García Iglesias
TI  - θ-Semisimple Classes of Type D in PSLn(q)
JO  - Journal of Lie Theory
PY  - 2016
SP  - 193
EP  - 218
VL  - 26
IS  - 1
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.887/
DO  - 10.5802/jolt.887
ID  - JOLT_2016_26_1_a9
ER  - 
%0 Journal Article
%A G. Carnovale
%A A. García Iglesias
%T θ-Semisimple Classes of Type D in PSLn(q)
%J Journal of Lie Theory
%D 2016
%P 193-218
%V 26
%N 1
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.887/
%R 10.5802/jolt.887
%F JOLT_2016_26_1_a9
G. Carnovale; A. García Iglesias. θ-Semisimple Classes of Type D in PSLn(q). Journal of Lie Theory, Volume 26 (2016) no. 1, pp. 193-218. doi: 10.5802/jolt.887

Cited by Sources: