Counting abelian group structures

Author:

Clarke Francis

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference8 articles.

1. Heuristics on class groups of number fields;Cohen, H.,1984

2. Euler, Leonhard, Introductio in analysin infinitorum, 1, Lausanne, 1748, Opera Omnia 8 B. G. Teubner, Geneva, 1922.

3. Hall, Philip, A partition formula connected with abelian groups, Comm. Math. Helv. 11 (1938/39), 126–129.

4. Die Grundlehren der mathematischen Wissenschaften, Band 114;Mac Lane, Saunders,1963

5. The algebra of partitions;Macdonald, I. G.,1984

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