Locally cyclic periodic group

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.