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

Finite p-groups in which the intersection of nonnormal subgroup and center has bounded order

Libo Zhaoa College of Mathematics, Guangdong University of Education, Guangzhou, ChinaView further author information
,
Yangming Lia College of Mathematics, Guangdong University of Education, Guangzhou, ChinaView further author information
,
Lü Gongb School of Sciences, Nantong University, Jiangsu, ChinaCorrespondence[email protected]
View further author information
&
Xiuyun Guoc Department of Mathematics, Shanghai University, Shanghai, ChinaView further author information
Pages 3825-3833 | Received 11 Dec 2022, Accepted 02 Mar 2023, Published online: 23 Mar 2023

References

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  • Rédei, L. (1974). Das schiefe Produkt in der Gruppentheorie mit Anwendung auf die endlichen nichtkommu- tativen Gruppen mit lauter kommutativen echten Untergruppen und die Ordnungszahlen,zu denen nur kommutative Gruppen gehören. Comment. Math. Helvet 20:225–264.
  • Lv, H., Zhou, W., Guo, X. (2011). Some finite 2-groups with index of every cyclic subgroup in its normal closure no greater than 4. J. Algebra 342:256–264.
  • Lv, H., Zhou, W., Yu, D. (2011). Some finite p-groups with bounded index of every cyclic subgroup in its normal closure. J. Algebra 338:169–179.
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  • Zhang, J., Zhang, Q. (2016). Finite p-groups all of whose minimal nonnormal subgroups posses large normal closures. Commun. Algebra 44:628–638.
  • Zhao, L., Guo, X. (2014). Finite p-groups in which the normal closures of nonnormal cyclic subgroups have small index. J. Algebra Appl. 13(2):13500871–13500877.
  • Zhao, L., Gong, L., Guo, X. (2021). Finite p-groups with a trivial core or the normal closure index p for every nonnormal abelian subgroup. Chin. Ann. Math. A 42(4):419–426.
  • Zhao, L., Li, Y., Gong, L. (2018). Finite groups in which the cores of every nonnormal subgroups are trivial. Publ. Math. Debreen 93(3–4):511–516.

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