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
