This paper mainly devotes to a problem of the number of sequencings for Abelian sequenceable groups by connecting basic properties of groups with combinatorial methemabics.

The paper has developed and perfected the information flowed method -a group orderingVmethod which was mentioned in paper [ 1 ] .

Sufficient and necessary conditions for supersolvable group;

Using the weakly c-normality of minimal subgroup of to characterize the structure of a finite group,some sufficient conditions of finite supersolvable group are obtained.

In this paper we prove:Let F be a saturated formation containing U,the class of all supersolvable groups and suppose that G is a group with a normal subgroup H such that G/H∈F.

The completely conditional permutability of minimal subgroups is used in this paper to obtain the sufficient condition for supersoluble groups: let G be a finite group, if every minimal subgroup and every cyclic subgroup of order 4 of G is completely c-permutable in G, G is supersoluble.

Using the concept,X-permutable subgroup of finite groups,two sufficient conditions of supersoluble groups are obtained:(1) G is a soluble group,let X be a subgroup of G such that X contains every maximal subgroup and every minimal subgroup of G.

In this paper,by using the concept of permutable subgroups,a new criterion of supersolubility of the product G=AB of finite supersoluble groups A and B is given.