  Let G be a finite group. A subgroup M of G is said to be an NR-subgroup if,
whenever K is normal in M, then K^G\cap M=K, where K^G is the normal closure of
K in G. Using the Classification of Finite Simple Groups, we prove that if
every maximal subgroup of G is an NR -subgroup then G is solvable. This gives a
positive answer to a conjecture posed in Berkovich (Houston J Math 24:631-638,
1998).
