EN
A note on finite groups with few TI-subgroups
Abstract
In [Comm. Algebra, 43(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
References
- S. Li, Z. Shen and N. Du, Finite groups with few TI-subgroups, Comm. Algebra, 43(7) (2015), 2680-2689.
- H. Mousavi, T. Rastgoo and V. Zenkov, The structure of non-nilpotent CTI- groups, J. Group Theory, 16(2) (2013), 249-261.
- D. J. S. Robinson, A Course in the Theory of Groups, Second Edition, Grad- uate Texts in Mathematics, 80, Springer-Verlag, New York, 1996.
- J. Shi and C. Zhang, Finite groups in which some particular subgroups are TI-subgroups, Miskolc Math. Notes, 14(3) (2013), 1037-1040.
Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Publication Date
January 11, 2018
Submission Date
June 10, 2016
Acceptance Date
-
Published in Issue
Year 2018 Volume: 23 Number: 23
APA
Shi, J., Huang, J., & Zhang, C. (2018). A note on finite groups with few TI-subgroups. International Electronic Journal of Algebra, 23(23), 42-46. https://doi.org/10.24330/ieja.373640
AMA
1.Shi J, Huang J, Zhang C. A note on finite groups with few TI-subgroups. IEJA. 2018;23(23):42-46. doi:10.24330/ieja.373640
Chicago
Shi, Jiangtao, Jingjing Huang, and Cui Zhang. 2018. “A Note on Finite Groups With Few TI-Subgroups”. International Electronic Journal of Algebra 23 (23): 42-46. https://doi.org/10.24330/ieja.373640.
EndNote
Shi J, Huang J, Zhang C (January 1, 2018) A note on finite groups with few TI-subgroups. International Electronic Journal of Algebra 23 23 42–46.
IEEE
[1]J. Shi, J. Huang, and C. Zhang, “A note on finite groups with few TI-subgroups”, IEJA, vol. 23, no. 23, pp. 42–46, Jan. 2018, doi: 10.24330/ieja.373640.
ISNAD
Shi, Jiangtao - Huang, Jingjing - Zhang, Cui. “A Note on Finite Groups With Few TI-Subgroups”. International Electronic Journal of Algebra 23/23 (January 1, 2018): 42-46. https://doi.org/10.24330/ieja.373640.
JAMA
1.Shi J, Huang J, Zhang C. A note on finite groups with few TI-subgroups. IEJA. 2018;23:42–46.
MLA
Shi, Jiangtao, et al. “A Note on Finite Groups With Few TI-Subgroups”. International Electronic Journal of Algebra, vol. 23, no. 23, Jan. 2018, pp. 42-46, doi:10.24330/ieja.373640.
Vancouver
1.Jiangtao Shi, Jingjing Huang, Cui Zhang. A note on finite groups with few TI-subgroups. IEJA. 2018 Jan. 1;23(23):42-6. doi:10.24330/ieja.373640