Main Page | See live article | Alphabetical index In abstract algebra, an ordered group is a group G that has the additional property that there exists a partial order "<" which is translation-invariant; in other words, "<" has the property that, for all a, b, and g in G, if a < b then ag < bg and ga < gb. See also linearly ordered group. This article is a stub. You can help Wikipedia by fixing it. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.