Bounds on the order of cross characteristic subgroups of the finite simple 
groups of Lie type
Proc. Amer. Math. Soc. 126 (1998), 3183-3189. 

Tihomir Asparouhov
California Institute of Technology, Pasadena, California 91125 


Abstract. Let $X(r)$ and $G(q)$ be finite groups of Lie type and $r$ and $q$ 
be coprime. If $G(q)$ is embedded in $X(r)$, then the 
Landazuri-Seitz-Zalesskii theorem implies that $G(q)$ is small relative to 
$X(r)$. We formalize this observation and illustrate how it can be used 
with some applications.