  A subgroup $H$ is said to be $nc$-supplemented in a group $G$ if there is a
subgroup $K\leq G$ such that $HK\unlhd G$ and $H\cap K$ is contained in $H_G$,
the core of $H$ in $G$. We characterize the solvability of finite groups $G$
with some subgroups of Sylow subgroups $nc$-supplemented in $G$. We also give a
result on $c$-supplemented subgroups.
