maximal condition

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

G_{1}\\subset G_{2}\\subset G_{3}\\subset\\cdots

is finite.

This is also called the ascending chain condition.

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

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

随便看

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。