A Remark on З-Permutability of Finite Groups  

作　　者：Li Fang WANG 

机构地区：[1]School of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China [2]Department of Mathematics, Shanxi Teachers University, Linfen 041004, P. R. China [3]Lingnan College and School of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China [4]Department of Mathematics, Nanchang University, Nanchang 330047, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2007年第11期1985-1990,共6页数学学报（英文版）

基　　金：Project supported by NSF of China(10571181);Advanced Academic Center of ZSU

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.

关 键 词：З-permutable subgroups supersolvable groups saturated formations 

分 类 号：O152[理学—数学]