Balanced group

Symbol-free definition
A finite group is said to be balanced if the Brauer core of the centralizer of any involution is contained in the Brauer core of the whole group.

Definition with symbols
A finite group $$G$$ is said to be balanced if $$O(C_G(t)) \le O(G)$$ for any $$t \in I(G)$$.

Stronger properties

 * Even-order solvable group