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Communications in Algebra Volume 51, 2023 - Issue 9
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Research Articles

Invariant TI-subgroups or subnormal subgroups and structure of finite groups

Jiakuan Lua School of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi, P. R. ChinaView further author information
,
Minghui Lia School of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi, P. R. ChinaView further author information
,
Boru Zhanga School of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi, P. R. ChinaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0001-5777-2683View further author information
ORCID Icon &
Wei Mengb School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi, P. R. ChinaView further author information
Pages 3703-3707 | Received 01 Nov 2022, Accepted 22 Feb 2023, Published online: 15 Mar 2023

References

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  • Beltra´n, A., Shao, C. (2019). Restrictions on maximal invariant subgroups implying solubility of finite groups. Ann. Math. Pura Appl. 198:357–366.
  • Guo, X., Li, S., Flavell, P. (2007). Finite groups whose abelian subgroups are TI-subgroups. J. Algebra 307:5656–5669.
  • Isaacs, I. M. (2008). Finite Group Theory. Providence, RI: American Mathematical Society.
  • Kurzweil, H., Stellmacher, B. (2004). The Theory of Finite Groups. Berlin-Heidelberg-New York: Springer-Verlag.
  • Lu, J., Guo, X. (2012). Finite groups all of whose second maximal subgroups are QTI-subgroups. Commun. Algebra 40:3726–3732.
  • Lu, J., Pang, L. (2012). A note on TI-subgroups of finite groups. Proc. Indian Acad. Sci. (Math. Sci.) 122:75–77.
  • Mousavi, H., Rastgoo, T., Zenkov, V. (2013). The structure of non-nilpotent CTI-groups. J. Group Theory 16: 249–261.
  • Monakhov, V. A., Trofimuk, A. B. (2014). Finite groups with subnormal non-cyclic subgroups. J. Group Theory 17:889–895.
  • Shao, C., Beltra´n, A. (2021). Invariant TI-subgroups and structure of finite groups. J. Pure Appl. Algebra 225:106566, 8 pp.
  • Shi, J., Zhang, C., Meng, W. (2013). On a finite group in which every non-abelian subgroup is a TI-subgroup. J. Algebra Appl. 12:1250178, 6 pp.
  • Shi, J., Zhang, C. (2014). A note on TI-subgroups of a finite group. Algebra Colloq. 21:343–346.
  • Walls, G. (1979). Trivial intersection groups. Arch. Math. 32:1–4.

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