TITLE: Sylow theorems for infinite groups 
QUESTION [8 upvotes]: Are there classes of infinite groups that admit Sylow subgroups and where the Sylow theorems  are valid ? 
More precisely, I'm looking for classes of groups $\mathcal{C}$ with the following properties: 

$\mathcal{C}$ includes the finite groups 
in $\mathcal{C}$ there is a notion of Sylow subgroups that coincides with the usual one when restricted to finite groups 
Sylow's theorems (or part of them) are valid in $\mathcal{C}$ 

An example of such a class $\mathcal{C}$ is given by the class of profinite groups.

REPLY [3 votes]: The best reference for this subject is the book of martyn Dixon: Locally finite groups and Sylow theory.