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单词 IsolatedSubgroup
释义

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

fg1gF.

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.

Theorem.

Let G be an abelianMathworldPlanetmath ordered group with order (http://planetmath.org/OrderGroup) 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.

References

  • 1 M. Larsen & P. McCarthy: Multiplicative theory of ideals.  Academic Press. New York (1971).
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更新时间:2025/5/4 21:10:50