Counting abelian group structures

Clarke, Francis

doi:10.1090/S0002-9939-06-08396-1

Counting abelian group structures
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by Francis Clarke

Proc. Amer. Math. Soc. 134 (2006), 2795-2799

DOI: https://doi.org/10.1090/S0002-9939-06-08396-1

Published electronically: April 10, 2006

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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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