Definition:Inverse System of Groups

Definition

Let $\sequence {G_n}_{n \mathop \in \N}$ be a sequence of groups.

For each $n \in \N$, let:

$\theta_{n + 1} : G_{n + 1} \to G_n$

be a homomorphism.

Then $\sequence {G_n}_{n \mathop \in \N}$ together with $\sequence {\theta_n}_{n \mathop \in \N_{>0} }$ is called an inverse system (of groups).

Sources

• 1969: M.F. Atiyah and I.G. MacDonald: Introduction to Commutative Algebra: Chapter $10$: Completion