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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 | References | Similar Articles | Additional Information

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

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.