maximal condition

A group is said to satisfy the maximal condition if every strictly ascending chain of subgroupsMathworldPlanetmathPlanetmath


is finite.

This is also called the ascending chain conditionMathworldPlanetmathPlanetmath.

A group satisfies the maximal condition if and only if the group and all its subgroups are finitely generatedMathworldPlanetmathPlanetmathPlanetmath.

Similar properties are useful in other classes of algebraic structuresPlanetmathPlanetmath: see for example the NoetherianPlanetmathPlanetmath condition for rings and modules.

Title maximal condition
Canonical name MaximalCondition
Date of creation 2013-03-22 13:58:47
Last modified on 2013-03-22 13:58:47
Owner mclase (549)
Last modified by mclase (549)
Numerical id 6
Author mclase (549)
Entry type Definition
Classification msc 20D30
Synonym ascending chain condition