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By weak c-supplement we investigated the possibility that a finite group is in a saturated formation containing all supersoluble groups. It was showed that for a saturated formation mathcalF containing all supersoluble groups, if there exists a group G such that G contins a normal subgroup N and G/N is supersoluble and if maximal subgroups of Sylow subgroups of N are c-supplemented in G, then Gin mathcalF. Some results are extended.