Finite Sylow subgroups in simple locally finite groups of Lie type

The main result of the paper is the following
Theorem. {\it Let $S=\{r_0,r_1,\dots,r_n\}$ be a finite nonempty set of primes and let $L$ be a Lie type of Chevalley groups. Then there exists a locally finite field $F$ of characteristic $r_0$ such that Sylow $r$-subgroups of the simple group $L(F)$ of type $L$ over $F$ are finite if and only if $r\notin S$.}