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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An application of blocks to torsion units in group rings
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by Andreas Bächle and Leo Margolis PDF
Proc. Amer. Math. Soc. 147 (2019), 4221-4231 Request permission

Abstract:

We use the theory of blocks of cyclic defect to prove that under a certain condition on the principal $p$-block of a finite group $G$, the normalized unit group of the integral group ring of $G$ contains an element of order $pq$ if and only if so does $G$ for $q$ a prime different from $p$. Using this we verify the Prime Graph Question for all alternating and symmetric groups and also for two sporadic simple groups.
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Additional Information
  • Andreas Bächle
  • Affiliation: Vakgroep Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
  • Email: andreas.bachle@vub.be
  • Leo Margolis
  • Affiliation: Vakgroep Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
  • MR Author ID: 1034185
  • Email: leo.margolis@vub.be
  • Received by editor(s): September 18, 2018
  • Received by editor(s) in revised form: January 8, 2019, and January 21, 2019
  • Published electronically: July 8, 2019
  • Additional Notes: Both authors are postdoctoral researchers of the Research Foundation Flanders (FWO - Vlaanderen).

  • Dedicated: One may dare to ask whether the theory of cyclic blocks can provide additional insight into Zassenhaus’ conjecture (ZC1). We have no clue, but...1
  • Communicated by: Pham Huu Tiep
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4221-4231
  • MSC (2010): Primary 16U60, 20C05, 20C20
  • DOI: https://doi.org/10.1090/proc/14561
  • MathSciNet review: 4002537