Main Page | See live article | Alphabetical index

Ordered group

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.