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

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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.

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References

  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)

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  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)

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Eszterházy Károly University, Leányka u. 4., Eger, 3300, Hungary

    Tibor Juhász

  2. Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, P7B 5E1, Canada

    Gregory T. Lee

  3. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

    Sudarshan K. Sehgal

  4. Dipartimento di Matematica “G. Castelnuovo”, Università degli Studi di Roma “La Sapienza”, P.le Aldo Moro n.5, 00185, Rome, Italy

    Ernesto Spinelli

Authors
  1. Tibor Juhász
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  2. Gregory T. Lee
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  3. Sudarshan K. Sehgal
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  4. Ernesto Spinelli
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Corresponding author

Correspondence to Gregory T. Lee.

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Presented by: Vyjayanthi Chari

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Juhász, T., Lee, G.T., Sehgal, S.K. et al. On the Lower Bound of the Derived Length of the Unit Group of a Nontorsion Group Algebra. Algebr Represent Theor 23, 457–466 (2020). https://doi.org/10.1007/s10468-019-09855-x

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  • DOI: https://doi.org/10.1007/s10468-019-09855-x

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