Let G be a finite group and H a subgroup of G. Recall that H is said to be aTI-subgroup ofG ifHg∩H = 1 or H for each b∈ G. In this note, we prove that if all non-nilpotent subgroups of a finite non-nilpotent group G...Let G be a finite group and H a subgroup of G. Recall that H is said to be aTI-subgroup ofG ifHg∩H = 1 or H for each b∈ G. In this note, we prove that if all non-nilpotent subgroups of a finite non-nilpotent group G are TI-subgroups, then G is soluble, and all non-nilpotent subgroups of G are normal.展开更多
基金The first author was supported by NSFC （Grant 11201401） and the China Postdoctoral Science Foundation （Grant 201104027）. The second author was supported by H.C. Orsted Postdoctoral Fellowship at DTU （Technical University of Denmark）.
文摘Let G be a finite group and H a subgroup of G. Recall that H is said to be aTI-subgroup ofG ifHg∩H = 1 or H for each b∈ G. In this note, we prove that if all non-nilpotent subgroups of a finite non-nilpotent group G are TI-subgroups, then G is soluble, and all non-nilpotent subgroups of G are normal.
基金中国博士后科学基金(No20100470136No201104027)+3 种基金"Agencija za raziskovalno dejavnost Republike Slovenije"projmladi raziskovalci"Agencija za raziskovalno dejavnost Republike Slovenije"research program P1-0285资助的项目
