Locally cyclic periodic group

From Groupprops
Jump to: navigation, search
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
View other group property conjunctions OR view all group properties


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