[[!redirects halving groups]] [[!redirects D-module]] [[!redirects D-modules]] [[!redirects D-bimodule]] [[!redirects D-bimodules]] ## Definition ## A **halving group** is an [[abelian group]] *G* 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 torsion-free halving group is a $\mathbb{D}$-[[bimodule]], where $\mathbb{D}$ are the [[dyadic rational numbers]]. * No halving group has characteristic $2$. ## See also * [[dyadic rational numbers]] * [[abelian group]] * [[torsion-free halving group]] ## External links * Wikipedia, [Halving](https://en.wikipedia.org/wiki/Halving)