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.

See also

• Descendant tree (group theory)

References