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Coclass

Mathematical concept

Mathematical concept

In mathematics, the coclass of a finite p-group of order p**n 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.

References

  • {{citation|mr=0583590
  • {{citation|mr=1277754
  • {{citation|mr=1258908
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