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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.
maximal condition is owned by Michael Clase.
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