Research Article
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Year 2018, Volume 23, Issue 23, 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, Volume 23, Issue 23, 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.

Details

Journal Section Articles
Authors

Jiangtao SHİ This is me


Jingjing HUANG This is me


Cui ZHANG This is me

Publication Date January 11, 2018
Published in Issue Year 2018, Volume 23, Issue 23

Cite

Bibtex @research article { ieja373640, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2018}, volume = {23}, number = {23}, pages = {42 - 46}, doi = {10.24330/ieja.373640}, title = {A note on finite groups with few TI-subgroups}, key = {cite}, author = {Shi, Jiangtao and Huang, Jingjing and Zhang, Cui} }
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 . DOI: 10.24330/ieja.373640
MLA Shi, J. , Huang, J. , Zhang, C. "A note on finite groups with few TI-subgroups" . International Electronic Journal of Algebra 23 (2018 ): 42-46 <https://dergipark.org.tr/en/pub/ieja/issue/33727/373640>
Chicago Shi, J. , Huang, J. , Zhang, C. "A note on finite groups with few TI-subgroups". International Electronic Journal of Algebra 23 (2018 ): 42-46
RIS TY - JOUR T1 - A note on finite groups with few TI-subgroups AU - JiangtaoShi, JingjingHuang, CuiZhang Y1 - 2018 PY - 2018 N1 - doi: 10.24330/ieja.373640 DO - 10.24330/ieja.373640 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 42 EP - 46 VL - 23 IS - 23 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.373640 UR - https://doi.org/10.24330/ieja.373640 Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Algebra A note on finite groups with few TI-subgroups %A Jiangtao Shi , Jingjing Huang , Cui Zhang %T A note on finite groups with few TI-subgroups %D 2018 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 23 %N 23 %R doi: 10.24330/ieja.373640 %U 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 2018): 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. 2018; 23(23): 42-46.
Vancouver Shi J. , Huang J. , Zhang C. A note on finite groups with few TI-subgroups. International Electronic Journal of Algebra. 2018; 23(23): 42-46.
IEEE J. Shi , J. Huang and C. Zhang , "A note on finite groups with few TI-subgroups", International Electronic Journal of Algebra, vol. 23, no. 23, pp. 42-46, Jan. 2018, doi:10.24330/ieja.373640