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[parent] procyclic group (Definition)
Definition 1   A group $ G$ is a procyclic group if $ G$ is a profinite group which is isomorphic to the inverse limit of some projective system of cyclic groups.
Example 1   The $ p$-adic integers $ \mathbb{Z}_p$ form a procyclic group since:
$\displaystyle \mathbb{Z}_p=\varprojlim \mathbb{Z}/p^n\mathbb{Z}.$



"procyclic group" is owned by alozano.
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Other names:  pro-cyclic group, pro-cyclic, procyclic

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Cross-references: cyclic groups, projective system, inverse limit, isomorphic, profinite group, group
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This is version 2 of procyclic group, born on 2005-03-23, modified 2005-06-01.
Object id is 6901, canonical name is ProcyclicGroup.
Accessed 2871 times total.

Classification:
AMS MSC: 20E18 (Group theory and generalizations :: Structure and classification of infinite or finite groups :: Limits, profinite groups)
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