A number of older papers by V.P. Platonov (in Russian, often followed by English translations) deal with periodic linear groups or linear algebraic groups in which the notions of Sylow theory make sense and where some results from the finite case actually generalize. One of the more substantial papers deals especially with conjugacy theorems:
The theory of algebraic linear groups and periodic groups. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 30 1966 573–620.
In other papers Platonov also works with classes of topological groups in a similar spirit.
P.S. Concerning sources, the long 1966 paper appears in an English translation (by the group theorist Kurt Hirsch) in volume 69 of the AMS Translations (Series 2), 1969; but this doesn't seem to be accessible online. There is a Google Scholar entry containing a full text PDF version of the Russian original here.