"On p-soluble groups and the number of simple
modules associated with a given Brauer pair
  --- Laurence Barker

We prove that, for a modular group algebra kG of
a p-soluble group G, the number of isomorphism
classes of simple kG-modules associated with a
given Brauer pair is a local invariant. This 
further refines Okuyama's refinement of the 
p-soluble case of the block form of Alperin's
conjecture.