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## A note on finite groups with few TI-subgroups

#### Jiangtao Shi [1] , Jingjing Huang [2] , Cui Zhang [3]

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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.
Non-metacyclic subgroup, TI-subgroup, normal, solvable, Sylow tower
• 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.
Konular Makaleler Yazar: Jiangtao Shi Yazar: Jingjing Huang Yazar: Cui Zhang
 Bibtex @araştırma makalesi { ieja373640, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2018}, volume = {23}, pages = {42 - 46}, doi = {10.24330/ieja.373640}, title = {A note on finite groups with few TI-subgroups}, key = {cite}, author = {Huang, Jingjing and Shi, Jiangtao 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 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 - Jiangtao Shi , Jingjing Huang , Cui Zhang 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 - http://dx.doi.org/10.24330/ieja.373640 Y2 - 2019 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 (Ocak 2018): 42-46. http://dx.doi.org/10.24330/ieja.373640