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Finite groups in which every non-nilpotent subgroup is a TI-subgroup or has p;'-order

  • Huixuan Ren and Jiangtao Shi EMAIL logo
Published/Copyright: December 15, 2022
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Abstract

We obtain a complete description of the structure of a finite group G in which every non-nilpotent subgroup is a TI-subgroup or has p -order for some fixed prime divisor p of | G | .

MSC 2010: 20D10

Award Identifier / Grant number: 11761079

Funding statement: This work was supported by Shandong Provincial Natural Science Foundation, China (ZR2017MA022 and ZR2020MA044) and NSFC (11761079).

References

[1] J. Lu, L. Pang and X. Zhong, Finite groups with non-nilpotent maximal subgroups, Monatsh. Math. 171 (2013), no. 3–4, 425–431. 10.1007/s00605-012-0432-7Search in Google Scholar

[2] D. J. S. Robinson, A Course in the Theory of Groups, 2nd ed., Grad. Texts in Math. 80, Springer, New York, 1996. 10.1007/978-1-4419-8594-1Search in Google Scholar

[3] C. Shao and A. Beltrán, Invariant TI-subgroups and structure of finite groups, J. Pure Appl. Algebra 225 (2021), no. 4, Paper No. 106566. 10.1016/j.jpaa.2020.106566Search in Google Scholar

[4] J. Shi, Finite groups in which every maximal subgroup is nilpotent or a TI-subgroup or has p -order, Algebra Colloq., to appear. Search in Google Scholar

[5] J. Shi and N. Li, Finite groups in which every self-centralizing subgroup is nilpotent or subnormal or a TI-subgroup, Czechoslovak Math. J. 71(146) (2021), no. 4, 1229–1233. 10.21136/CMJ.2021.0512-20Search in Google Scholar

[6] J. Shi, N. Li and R. Shen, Finite groups in which every maximal subgroup is nilpotent or normal or has p -order, preprint (2022), https://arxiv.org/abs/2202.02322. Search in Google Scholar

[7] J. Shi and C. Zhang, A note on TI-subgroups of a finite group, Algebra Colloq. 21 (2014), no. 2, 343–346. 10.1142/S1005386714000297Search in Google Scholar

[8] L. Shirong, Finite non-nilpotent groups all of whose second maximal subgroups are TI-groups, Math. Proc. R. Ir. Acad. 100A (2000), no. 1, 65–71. Search in Google Scholar

[9] G. Walls, Trivial intersection groups, Arch. Math. (Basel) 32 (1979), no. 1, 1–4. 10.1007/BF01238459Search in Google Scholar

Received: 2022-04-17
Revised: 2022-07-11
Accepted: 2022-08-28
Published Online: 2022-12-15
Published in Print: 2023-04-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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