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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Counting abelian group structures


Author: Francis Clarke
Journal: Proc. Amer. Math. Soc. 134 (2006), 2795-2799
MSC (2000): Primary 20K01; Secondary 20D60, 20K35, 20K40
Published electronically: April 10, 2006
MathSciNet review: 2231600
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08396-1
PII: S 0002-9939(06)08396-1
Received by editor(s): April 15, 2005
Published electronically: April 10, 2006
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.