Definition:Inverse System of Groups
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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