isolated subgroup

Let G be a ordered group and F its subgroupMathworldPlanetmathPlanetmath.  We call this subgroup if every element f of F and every element g of G satisfy


If an ordered group G has only a finite number of isolated subgroups, then the number of proper (G) isolated subgroups of G is the of G.


Let G be an abelianMathworldPlanetmath ordered group with order ( at least 2.  The of G equals one iff there is an order-preserving isomorphismPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath from G onto some subgroup of the multiplicative groupMathworldPlanetmath of real numbers.


  • 1 M. Larsen & P. McCarthy: Multiplicative theory of ideals.  Academic Press. New York (1971).
Title isolated subgroup
Canonical name IsolatedSubgroup
Date of creation 2013-03-22 14:55:08
Last modified on 2013-03-22 14:55:08
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 13
Author pahio (2872)
Entry type Definition
Classification msc 20F60
Classification msc 06A05
Related topic RankOfValuation
Related topic KrullValuation
Defines rank of ordered group