In mathematics, the coclass of a finite p-group of order pn is n − 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. See also Descendant tree (group theory) References P-groups