Groups of prime-square order
Let be a prime number. There are two groups of order , namely:
|Group name||Symbols typically used for group||Description of group|
|cyclic group of prime-square order||cyclic group whose order is|
|elementary abelian group of prime-square order||, ,||elementary abelian group whose order is|
Both of these are abelian groups.
For a proof that these are the only groups of prime-square order, see classification of groups of prime-square order.
|Value of prime number||Cyclic group of order||Elementary abelian group of order|
|2||cyclic group:Z4||Klein four-group|
|3||cyclic group:Z9||elementary abelian group:E9|
|5||cyclic group:Z25||elementary abelian group:E25|