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On the Lower Bound of the Derived Length of the Unit Group of a Nontorsion Group Algebra

  • Tibor Juhász
  • Gregory T. LeeEmail author
  • Sudarshan K. Sehgal
  • Ernesto Spinelli
Article
  • 14 Downloads

Abstract

Let G be a nonabelian nilpotent group and F a field of characteristic p > 2, such that the unit group \(\mathcal {U}(FG)\) of the group ring FG is solvable and G contains a p-element. Here we provide a lower bound for the derived length of \(\mathcal {U}(FG)\) that corrects the result from Lee et al. (Algebr. Represent. Theory 17, 1597–1601 2014) when G is nontorsion and \(G^{\prime }\) is a finite p-group.

Keywords

Group ring Unit group Derived length 

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Notes

References

  1. 1.
    Juhász, T.: The derived length of the unit group of a group algebra—the case \(G^{\prime }=Syl_{p}(G)\). J. Algebra Appl. 16(1750142), 7 (2017)zbMATHGoogle Scholar
  2. 2.
    Lee, G.T, Sehgal, S.K., Spinelli, E.: Group rings with solvable unit groups of minimal derived length. Algebr. Represent. Theory 17, 1597–1601 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Robinson, D.J.S.: A course in the theory of groups, 2nd ed. Springer, New York (1996)Google Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  • Tibor Juhász
    • 1
  • Gregory T. Lee
    • 2
    Email author
  • Sudarshan K. Sehgal
    • 3
  • Ernesto Spinelli
    • 4
  1. 1.Institute of Mathematics and InformaticsEszterházy Károly UniversityEgerHungary
  2. 2.Department of Mathematical SciencesLakehead UniversityThunder BayCanada
  3. 3.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  4. 4.Dipartimento di Matematica “G. Castelnuovo”Università degli Studi di Roma “La Sapienza”RomeItaly

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