Restricted Burnside group

Definition
The restricted Burnside group $$RB(n,d)$$, sometimes denoted $$R(n,d)$$, is defined as the quotient group by the finite residual of the Burnside group $$B(n,d)$$. In other words, it is the quotient of $$B(n,d)$$ by the intersection of all normal subgroups of finite index in it.

Note that this group is a finite group if and only if the restricted Burnside problem for the pair $$(n,d)$$ has the answer Yes.

Facts

 * Kostrikin's theorem on restricted Burnside problem: For any prime number $$p$$, the group $$RB(n,p)$$ is finite for every value of $$n$$.
 * The condition that this group be finite is weaker than the condition that the Burnside group $$B(n,d)$$ be finite, i.e., there are many cases where $$B(n,d)$$ is known to be infinite and $$RB(n,d)$$ is known to be finite. This includes all odd primes greater than 665.
 * In those cases where $$B(n,d)$$ is finite, $$RB(n,d)$$ is isomorphic to $$B(n,d)$$.