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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 that has nilpotency class c, and order pc + 1, where p is a prime number and c > 1. Equivalently, it has the following properties:
- The abelianization of the group, i.e., 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
