Coclass

In mathematics, the coclass of a finite p-group of order pn is n &minus; c, where c is the 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.