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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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Counting abelian group structures
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by Francis Clarke PDF
Proc. Amer. Math. Soc. 134 (2006), 2795-2799 Request permission

Abstract:

A bijective proof is given of a recurrence for the function counting the number of binary operations which endow a finite set with the structure of an abelian group. The proof depends on a lemma in “labelled homological algebra” and provides a simple route to a “curious result” of Philip Hall.
References
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Additional Information
  • Francis Clarke
  • Affiliation: Department of Mathematics, University of Wales Swansea, Swansea SA2 8PP, Wales
  • Email: F.Clarke@Swansea.ac.uk
  • Received by editor(s): April 15, 2005
  • Published electronically: April 10, 2006
  • Communicated by: Jonathan I. Hall
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 2795-2799
  • MSC (2000): Primary 20K01; Secondary 20D60, 20K35, 20K40
  • DOI: https://doi.org/10.1090/S0002-9939-06-08396-1
  • MathSciNet review: 2231600