  In this paper, we investigate the difference between weak second maximal
subgroups and second maximal subgroups. A sufficient and necessary condition is
also given to describe such class of groups whose weak second maximal subgroups
coincide with its second maximal subgroups(called WSM-groups) under the
solvable case. As an application, we show that every non-vanishing element of a
solvable WSM-group lies in its Fitting subgroup.
