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A note on the solvability of a finite group in which every non-nilpotent maximal subgroup is normal

Year 2023, Volume: 34 Issue: 34, 207 - 209, 10.07.2023

Wenjing Lıu Jiangtao Shı Yunfeng Tıan

https://doi.org/10.24330/ieja.1252751

Abstract

We provide a new and simple proof to show that a finite group in which every non-nilpotent maximal subgroup is normal is solvable.

Keywords

Non-nilpotent maximal subgroup solvable group normal subgroup of prime-power order

References

  • N. Li and J. Shi, A note on a finite group with all non-nilpotent maximal subgroups being normal, Ital. J. Pure Appl. Math., 42 (2019), 700-702.
  • D. J. S. Robinson, A Course in the Theory of Groups (Second Edition), Springer-Verlag, New York, 1996.
  • J. Shi, A finite group in which all non-nilpotent maximal subgroups are normal has a Sylow tower, Hokkaido Math. J., 48(2) (2019), 309-312.

Year 2023, Volume: 34 Issue: 34, 207 - 209, 10.07.2023

Wenjing Lıu Jiangtao Shı Yunfeng Tıan

https://doi.org/10.24330/ieja.1252751

Abstract

Keywords

Non-nilpotent maximal subgroup solvable group normal subgroup of prime-power order

References

  • N. Li and J. Shi, A note on a finite group with all non-nilpotent maximal subgroups being normal, Ital. J. Pure Appl. Math., 42 (2019), 700-702.
  • D. J. S. Robinson, A Course in the Theory of Groups (Second Edition), Springer-Verlag, New York, 1996.
  • J. Shi, A finite group in which all non-nilpotent maximal subgroups are normal has a Sylow tower, Hokkaido Math. J., 48(2) (2019), 309-312.
There are 3 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Wenjing Lıu This is me

Jiangtao Shı This is me

Yunfeng Tıan This is me

Early Pub Date May 11, 2023
Publication Date July 10, 2023
Published in Issue Year 2023 Volume: 34 Issue: 34

Cite

APA Lıu, W., Shı, J., & Tıan, Y. (2023). A note on the solvability of a finite group in which every non-nilpotent maximal subgroup is normal. International Electronic Journal of Algebra, 34(34), 207-209. https://doi.org/10.24330/ieja.1252751
AMA Lıu W, Shı J, Tıan Y. A note on the solvability of a finite group in which every non-nilpotent maximal subgroup is normal. IEJA. July 2023;34(34):207-209. doi:10.24330/ieja.1252751
Chicago Lıu, Wenjing, Jiangtao Shı, and Yunfeng Tıan. “A Note on the Solvability of a Finite Group in Which Every Non-Nilpotent Maximal Subgroup Is Normal”. International Electronic Journal of Algebra 34, no. 34 (July 2023): 207-9. https://doi.org/10.24330/ieja.1252751.
EndNote Lıu W, Shı J, Tıan Y (July 1, 2023) A note on the solvability of a finite group in which every non-nilpotent maximal subgroup is normal. International Electronic Journal of Algebra 34 34 207–209.
IEEE W. Lıu, J. Shı, and Y. Tıan, “A note on the solvability of a finite group in which every non-nilpotent maximal subgroup is normal”, IEJA, vol. 34, no. 34, pp. 207–209, 2023, doi: 10.24330/ieja.1252751.
ISNAD Lıu, Wenjing et al. “A Note on the Solvability of a Finite Group in Which Every Non-Nilpotent Maximal Subgroup Is Normal”. International Electronic Journal of Algebra 34/34 (July 2023), 207-209. https://doi.org/10.24330/ieja.1252751.
JAMA Lıu W, Shı J, Tıan Y. A note on the solvability of a finite group in which every non-nilpotent maximal subgroup is normal. IEJA. 2023;34:207–209.
MLA Lıu, Wenjing et al. “A Note on the Solvability of a Finite Group in Which Every Non-Nilpotent Maximal Subgroup Is Normal”. International Electronic Journal of Algebra, vol. 34, no. 34, 2023, pp. 207-9, doi:10.24330/ieja.1252751.
Vancouver Lıu W, Shı J, Tıan Y. A note on the solvability of a finite group in which every non-nilpotent maximal subgroup is normal. IEJA. 2023;34(34):207-9.