nLab halving group

Contents

Contents

Idea

An abelian group where one could halve each element or divide each element by two.

Definition

A halving group is an abelian group G with a function ()/2:GG(-)/2:G \to G called halving or dividing by two such that for all gGg \in G, g/2+g/2=gg/2 + g/2 = g.

Properties

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

  • The only element of a halving group with order 22 is the additive unit 00.

See also

Created on June 17, 2022 at 19:26:28. See the history of this page for a list of all contributions to it.