Definition- A group $G$ is said to be locally finite if every finite subset of $G$ generates a finite subgroup.
Now I have to prove the following proposition.
Proposition- Let $G$ be a locally finite nilpotent group. Then $G=\times\ O_p$ where $O_p$ is the normal maximal $p$ - subgroup of $G$ and direct product is taken over all primes $p$.
I have encountered locally finite groups for first time and any help on this proposition is appreciated.
I know that for finite nilpotent groups, $G$ can be expressed as direct product of nontrivial sylow subgroups, but here in locally finite nilpotent, sylow subgroups (maximal p-groups) can be infinite too.
If you can give a reference of this proof, it will be a huge help. Thanks.