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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Definition

A group is termed a locally cyclic periodic group if it satisfies the following equivalent conditions:

1. It is a locally cyclic group as well as a periodic group: every element has finite order.
2. It is isomorphic to a restricted direct product of groups, where for each prime $p$, there is either one cyclic group of order a power of $p$ appearing or one p-quasicyclic group appearing.

Equivalence of definitions

Further information: Equivalence of definitions of locally cyclic periodic group