Locally graded groups with all non-nilpotent subgroups permutable, II

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ATLIHAN S., Dixon M. R., Evans M. J.

Journal of Algebra, vol.641, pp.530-533, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 641
  • Publication Date: 2024
  • Doi Number: 10.1016/j.jalgebra.2023.11.008
  • Journal Name: Journal of Algebra
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.530-533
  • Keywords: Nilpotent group, Permutable subgroup, Quasihamiltonian group
  • Gazi University Affiliated: Yes

Abstract

Let G be a locally graded group and suppose that every non-nilpotent subgroup of G is permutable. We prove that G is soluble. (In light of previous results of the authors, it suffices to prove that G is soluble if it is periodic.)