A note on finite groups with few TI-subgroups

Authors : Jiangtao SHİ, Jingjing HUANG, Cui ZHANG

Pages : 42-46

Doi:10.24330/ieja.373640

View : 15 | Download : 10

Publication Date : 2018-01-11

Article Type : Research Paper

Abstract :In [Comm. Algebra, 43insert ignore into journalissuearticles values(2015);, 2680-2689], nite groups all of whose metacyclic subgroups are TI-subgroups have been classi ed by S. Li, Z. Shen and N. Du. In this note we investigate a nite group all of whose non-metacyclic subgroups are TI-subgroups. We prove that G is a group all of whose non-metacyclic subgroups are TI-subgroups if and only if all non- metacyclic subgroups of G are normal. Furthermore, we show that a group all of whose non-cyclic subgroups are TI-subgroups has a Sylow tower.
Keywords : Non metacyclic subgroup, TI subgroup, normal, solvable, Sylow tower