Small intersections of principal blocks

In this note, it is shown that a finite group G is solvable if for each odd prime divisor p of |G|, |Irr(B0(G)2)∩Irr(B0(G)p)|≤2, where Irr(B0(G)p) is the set of complex irreducible characters of the principal p-block B0(G)p of G. Also, the structure of such groups is investigated. Examples show that the bound 2 is best possible.