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Communications in Algebra Volume 49, 2021 - Issue 9
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Articles

On the generalized norms of a group

Yuan LinCollege of Science, China Agricultural University, Beijing, ChinaView further author information
,
Yicheng GongCollege of Science, China Agricultural University, Beijing, ChinaView further author information
&
Zhencai ShenCollege of Science, China Agricultural University, Beijing, ChinaCorrespondence[email protected]
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Pages 4092-4097 | Received 22 Oct 2020, Accepted 30 Mar 2021, Published online: 28 Apr 2021

References

  • Baer, R., Der, K. (1935). Eine Charkteristishe Untergruppe. Compos. Math. 1:254–283.
  • Baer, R. (1956). Norm and hypernorm. Publ. Math. Debrecen. 4:347–350.
  • Ballester Bolinches, A., Kamornikov, S. F., Meng, H. (2017). Normalisers of residuals of finite groups. Arch. Math. 109(4):305–310. DOI: 10.1007/s00013-017-1074-8.
  • Fu, C., Shen, Z., Yan, Q. (2020). The norm of p-decomposable residuals of all subgroups in a finite group. J. Algebra Appl. 19(6):2050109–2050109. DOI: 10.1142/S0219498820501091.
  • Gong, L., Isaacs, I. M. (2017). Normalizers of nilpotent residuals. Arch. Math. 108(1):1–7. DOI: 10.1007/s00013-016-0995-y.
  • Guo, W. (2000). The Theory of Classes of Groups. Beijing-New York-Dordrecht-Boston-London: Science Press, Kluwer Academic Publishers.
  • Huppert, B. (1987). Endliche Gruppen I. Berlin-Heidelberg-New York: Springer Verlag.
  • Lewis, M. L., Zarrin, M. (2019). Generalizing Baers norm. J. Group Theory 22(1):157–168. DOI: 10.1515/jgth-2018-0031.
  • Li, S., Shen, Z. (2010). On the intersection of normalizers of direved subgroups of all subgroups of a finite group. J. Algebra 323(5):1349–1357. DOI: 10.1016/j.jalgebra.2009.12.015.
  • Li, X., Guo, X. (2015). On the normalizers of p-nilpotency-residuals of all subgroups in a finite group. J. Algebra Appl. 14(10):1550146–1550151. DOI: 10.1142/S0219498815501467.
  • Miller, G. A., Moreno, H. C. (1903). Non-abelian groups in which every subgroup is abelian. Trans. Amer. Math. Soc. 4(4):398–404. DOI: 10.1090/S0002-9947-1903-1500650-9.
  • Robinson, D. J. S. (1982). A Course in the Theory of Groups. New York: Springer-Verlag.
  • Shen, Z., Shi, W., Qian, G. (2012). On the norm of the nilpotent residuals of all subgroups of a finite group. J. Algebra 352(1):290–298. DOI: 10.1016/j.jalgebra.2011.11.018.
  • Shen, Z., Li, S., Zhang, J. (2012). On the derived norms of a finite group. Ukr. Math. J. 68(2017):1184–1191.
  • Shen, Z., Zhang, J., Shi, W. (2013). On a generalization of Hamiltonian groups and a dualization of PN-groups. Commun. Algebra 41(5):1608–1618. DOI: 10.1080/00927872.2011.644609.
  • Shen, Z., Shi, W., Zhang, J. (2011). Finite non-nilpotent generalizations of Hamiltonian groups. Bull. Korean Math. Soc. 48(6):1147–1155. DOI: 10.4134/BKMS.2011.48.6.1147.
  • Shen, Z., Li, S. (2014). On the F-residuals norm of a group. J. Algebra Appl. 13:1–6.
  • Su, N., Wang, Y. (2013). On the normalizers of F-residuals of all subgroups of a finite group. J. Algebra 392:185–198.
  • Thompson, J.G. (1968). Nonsolvable finite groups all of whose local subgroups are solvable. Bull. Amer. Math. Soc. 74(3):383–437. DOI: 10.1090/S0002-9904-1968-11953-6.

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