  The famous Brauer-Fowler theorem states that the order of a finite simple
group can be bounded in terms of the order of the centralizer of an involution.
Using the classification of finite simple groups, we generalize this theorem
and prove that if a simple locally finite group has an involution which
commutes with at most $n$ involutions, then the group is finite and its order
is bounded in terms of $n$ only. This answers a question of Strunkov from the
Kourovka notebook.
