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Definition

A halving group is an abelian groupG with a function $(-)/2:G \to G$ called halving and a dependent function

$p:\prod_{g:G} g/2 + g/2 = g$

Properties

Just as every abelian group is a $\mathbb{Z}$-bimodule, every halving group is a $\mathbb{D}$-bimodule, where $\mathbb{D}$ are the dyadic rational numbers?.