摘要
Let З be a complete set of Sylow subgroups of a finite group G, that is, З contains exactly one and only one Sylow p-subgroup of G for each prime p. A subgroup of a finite group G is said to be З-permutable if it permutes with every member of З. Recently, using the Classification of Finite Simple Groups, Heliel, Li and Li proved tile following result: If the cyclic subgroups of prime order or order 4 iif p = 2) of every member of З are З-permutable subgroups in G, then G is supersolvable.In this paper, we give an elementary proof of this theorem and generalize it in terms of formation.
Let З be a complete set of Sylow subgroups of a finite group G, that is, З contains exactly one and only one Sylow p-subgroup of G for each prime p. A subgroup of a finite group G is said to be З-permutable if it permutes with every member of З. Recently, using the Classification of Finite Simple Groups, Heliel, Li and Li proved tile following result: If the cyclic subgroups of prime order or order 4 iif p = 2) of every member of З are З-permutable subgroups in G, then G is supersolvable.In this paper, we give an elementary proof of this theorem and generalize it in terms of formation.
基金
Project supported by NSF of China(10571181)
Advanced Academic Center of ZSU