Coclass

In mathematics, the coclass of a finite p-group of order pⁿ is n − c where c is the nilpotency class.

The coclass conjectures

The coclass conjectures were introduced by and proved by and. They are:

Conjecture A: Every p-group has a normal subgroup of class 2 with index depending only on p and its coclass.
Conjecture B: The solvable length of a p-group can be bounded in terms of p and the coclass.
Conjecture C: A pro p-group of finite coclass is solvable.
Conjecture D: There are only finitely many pro p-groups of given coclass.
Conjecture E: There are only finitely many solvable pro p-groups of given coclass.