Coclass Explained
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
