Groupprops, The Group Properties Wiki (pre-alpha)
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P-group
From Groupprops
Contents |
Definition
Let p be a prime. A p-group is a group in which every element has finite order, and the order of every element is a power of p.
The term p-group is typically used for a finite p-group, which is equivalent to a group of prime power order.
Relation with other properties
Stronger properties
- Group of prime power order
- Nilpotent p-group: For proof of the implication, refer and for proof of its strictness (i.e. the reverse implication being false) refer p-group not implies nilpotent.
Weaker properties
