Similar to the influence on nilpotent residual of the totally permutability of subgroups,naturally,we can study their influence on σ-nilpotent residual when nilpotent groups are generalized to σ-nilpotent groups.The intersection of all normal subgroups N of G such that G/N is σ-nilpotent is called σ-nilpotent residual of G,and is denoted as . Let G=AB, where A and B are totally permutable subgroups of G,this paper gives some new conclusions that B normalises and centralises by using the concepts and theories of σ-nilpotent subgroups and σ-supersoluble subgroups,and by applying some properties and methods of complete Hall σ-set and finite group theory.
Received: 07 April 2022
Published: 10 January 2024
Zhijie SHI,Yuemei MAO,Xiaojian MA. The influence of the totally permutability of subgroups on σ-nilpotent residual. Journal of Zhejiang University (Science Edition), 2024, 51(1): 1-4.
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