Hilbert's theorem 90 for finite nilpotent groups

Document Type : Research Paper

Author

Department of Mathematics, University of Wisconsin Madison, WI, USA

Abstract

‎In this note we prove an analog of Hilbert's theorem 90 for finite nilpotent groups‎. ‎Our version of Hilbert's theorem 90 was inspired by the Boston--Bush--Hajir (BBH) heuristics in number theory and will be useful in extending the BBH heuristics beyond quadratic field extensions‎.

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References

[1] N. Boston, M. R. Bush and F. Hajir, Heuristics for p-class towers of imaginary quadratic fields, Math. Annalen., 368
(2017) 633–669.
[2] I. M. Isaacs, Finite Group Theory, Graduate Studies in Mathematics, 92, Providence, RI: American Mathematical
Society, 2008.
[3] C. Quadrelli and T. Weigel, A group-theoretical version of Hilbert’s theorem 90, Bull. London Math. Soc., 47 (2015)
704–714.

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History

  • Receive Date: 04 April 2019
  • Revise Date: 12 October 2019
  • Accept Date: 13 August 2019
  • Published Online: 01 June 2021

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