The Group Properties Wiki (pre-alpha)
TIP: Read more about how the definition in Groupprops is structured
ABOUT US: Read our purpose statement and learn what makes us special
ALSO CHECK OUT: Diffgeom: The Differential Geometry Wiki
Maximal class group
From Groupprops
The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter
Definition
A maximal class group is a group of prime power order with the following special structure:
- The group has nilpotence class c, and order pc + 1, where p is a prime number
- The quotient of the group by its commutator subgroup has order p2
- The upper central series and lower central series coincide, and all the successive quotients (except the top-most quotient) are of order p
Relation with other properties
Weaker properties

