Geodesic
$A_{1}$-TYPE SUBGROUPS CONTAINING REGULAR UNIPOTENT ELEMENTS
Forum of Mathematics, Sigma, Tome 7 (2019)

Voir la notice de l'article provenant de la source Cambridge University Press

Let $G$ be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic $p>0$ and let $X=\text{PSL}_{2}(p)$ be a subgroup of $G$ containing a regular unipotent element $x$ of $G$. By a theorem of Testerman, $x$ is contained in a connected subgroup of $G$ of type $A_{1}$. In this paper we prove that with two exceptions, $X$ itself is contained in such a subgroup (the exceptions arise when $(G,p)=(E_{6},13)$ or $(E_{7},19)$). This extends earlier work of Seitz and Testerman, who established the containment under some additional conditions on $p$ and the embedding of $X$ in $G$. We discuss applications of our main result to the study of the subgroup structure of finite groups of Lie type. 
@article{10_1017_fms_2019_12,
     author = {TIMOTHY C. BURNESS and DONNA M. TESTERMAN},
     title = {$A_{1}${-TYPE} {SUBGROUPS} {CONTAINING} {REGULAR} {UNIPOTENT} {ELEMENTS}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {7},
     year = {2019},
     doi = {10.1017/fms.2019.12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2019.12/}
}
TY  - JOUR
AU  - TIMOTHY C. BURNESS
AU  - DONNA M. TESTERMAN
TI  - $A_{1}$-TYPE SUBGROUPS CONTAINING REGULAR UNIPOTENT ELEMENTS
JO  - Forum of Mathematics, Sigma
PY  - 2019
VL  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2019.12/
DO  - 10.1017/fms.2019.12
LA  - en
ID  - 10_1017_fms_2019_12
ER  - 
%0 Journal Article
%A TIMOTHY C. BURNESS
%A DONNA M. TESTERMAN
%T $A_{1}$-TYPE SUBGROUPS CONTAINING REGULAR UNIPOTENT ELEMENTS
%J Forum of Mathematics, Sigma
%D 2019
%V 7
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2019.12/
%R 10.1017/fms.2019.12
%G en
%F 10_1017_fms_2019_12
TIMOTHY C. BURNESS; DONNA M. TESTERMAN. $A_{1}$-TYPE SUBGROUPS CONTAINING REGULAR UNIPOTENT ELEMENTS. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.12

Cité par Sources :