Locally graded groups with all non-nilpotent subgroups permutable

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

Journal of Algebra, vol.632, pp.62-69, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 632
  • Publication Date: 2023
  • Doi Number: 10.1016/j.jalgebra.2023.05.020
  • Journal Name: Journal of Algebra
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.62-69
  • Keywords: Nilpotent group, Permutable subgroup, Quasihamiltonian group
  • Gazi University Affiliated: Yes

Abstract

The authors prove the following results: Let G be a locally graded group and suppose that every non-nilpotent subgroup of G is permutable. If G is torsion-free, then G is nilpotent. If G is non-periodic, then G is soluble.