Title of article :
A note on finite groups with few TI-subgroups
Author/Authors :
Shi, Jiangtao School of Mathematics and Information Science - Yantai University, China , Zhang, Cui School of Mathematics and Information Science - Yantai University, China , Huang, Jingjing Faculty of Science and Technology Communication - University of China, China
Abstract :
In [Comm. Algebra, 43(2015), 2680-2689], finite groups all of
whose metacyclic subgroups are TI-subgroups have been classified by S. Li,
Z. Shen and N. Du. In this note we investigate a finite 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 nonmetacyclic 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
Journal title :
International Electronic Journal of Algebra
