Kummer structures

Details Kummer structures Kummer structures

2008-06-02

arxiv.org/abs/0806.0409v1

Mathematics

Group Theory

15 pages

Scientific paper

Suppose we take an abelian group G and quotient it by the action of negation. What structure does the quotient K inherit from the group structure of G? We describe this structure (which we call the Kummer of G) in terms of a map from the set of unordered pairs of elements of K to itself. We propose some axioms that hold for such structures, and show that every structure satisfying those axioms either is the Kummer of a unique group, or comes from one other construction, the quotient of a 2-torsion group by an involution.

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