I asked this question as a comment on this old, probably abandoned question about the Fitting subgroup $F(G)$ of a group $G$.
It was stated in the question that
$F(G)$ is the product of all $O_p(G)$ for all prime $p$.
(Edit: Derek Holt pointed out below that $G$ must be finite here.)
I'm just curious. I couldn't find the notation in any of the obvious places, like in the results of a simple Google search. I'm interested in the theorem quoted above.
The closest thing I've seen before is the notation for the ring of integers in the context of algebraic number theory, which is way off.
$O_p(G)$ is the $p$-core of the finite group $G$. This is the intersection of all its Sylow $p$-subgroups, and is the largest normal $p$-subgroup of $G$.