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Year 2018, , 42 - 46, 11.01.2018
https://doi.org/10.24330/ieja.373640

Abstract

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.

A note on finite groups with few TI-subgroups

Year 2018, , 42 - 46, 11.01.2018
https://doi.org/10.24330/ieja.373640

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.

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.
There are 4 citations in total.

Details

Journal Section Articles
Authors

Jiangtao Shi This is me

Jingjing Huang This is me

Cui Zhang This is me

Publication Date January 11, 2018
Published in Issue Year 2018

Cite

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 Shi J, Huang J, Zhang C. A note on finite groups with few TI-subgroups. IEJA. January 2018;23(23):42-46. doi:10.24330/ieja.373640
Chicago Shi, Jiangtao, Jingjing Huang, and Cui Zhang. “A Note on Finite Groups With Few TI-Subgroups”. International Electronic Journal of Algebra 23, no. 23 (January 2018): 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 J. Shi, J. Huang, and C. Zhang, “A note on finite groups with few TI-subgroups”, IEJA, vol. 23, no. 23, pp. 42–46, 2018, doi: 10.24330/ieja.373640.
ISNAD Shi, Jiangtao et al. “A Note on Finite Groups With Few TI-Subgroups”. International Electronic Journal of Algebra 23/23 (January 2018), 42-46. https://doi.org/10.24330/ieja.373640.
JAMA 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, 2018, pp. 42-46, doi:10.24330/ieja.373640.
Vancouver Shi J, Huang J, Zhang C. A note on finite groups with few TI-subgroups. IEJA. 2018;23(23):42-6.