Locally cyclic periodic group
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: locally cyclic group and periodic group
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A group is termed a locally cyclic periodic group if it satisfies the following equivalent conditions:
- It is a locally cyclic group as well as a periodic group: every element has finite order.
- It is isomorphic to a restricted direct product of groups, where for each prime , there is either one cyclic group of order a power of appearing or one p-quasicyclic group appearing.
Equivalence of definitions
Further information: Equivalence of definitions of locally cyclic periodic group