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From examples to methods: two cases from the study of units in integral group rings

Author

Listed:
  • Andreas Bächle

    (Vrije Universiteit Brussel)

  • Leo Margolis

    (Vrije Universiteit Brussel)

Abstract

In this article, we review the proofs of the first Zassenhaus Conjecture on conjugacy of torsion units in integral group rings for the alternating groups of degree 5 and 6, by Luthar-Passi and Hertweck. We describe how the study of these examples led to the development of two methods – the HeLP method and the lattice method. We exhibit these methods and summarize some results which were achieved using them. We then apply these methods to the study of the first Zassenhaus conjecture for the alternating group of degree 7 where only one critical case remains open for a full answer. Along the way we show in examples how recently obtained results can be combined with the methods presented and collect open problems some of which could be attacked using these methods.

Suggested Citation

  • Andreas Bächle & Leo Margolis, 2021. "From examples to methods: two cases from the study of units in integral group rings," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(3), pages 669-686, September.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:3:d:10.1007_s13226-021-00180-y
    DOI: 10.1007/s13226-021-00180-y
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