Cyclic group of prime power order

Definition
A cyclic group of prime power order is a group satisfying the following equivalent conditions:


 * 1) It is cyclic and its order is a power of a prime.
 * 2) It is isomorphic to the group of integers modulo a power of a prime.
 * 3) It is not generated by its proper subgroups.

Note that this definition excludes the trivial group.

Stronger properties

 * Weaker than::Group of prime order

Weaker properties

 * Stronger than::Finite cyclic group