Enumeration of nilpotent loops via cohomology

The isomorphism problem for centrally nilpotent loops call be tackled by methods of cohomology. We develop tools based oil cohomology and linear algebra that either lend themselves to direct count of the isomorphism classes (notably in the case of nilpotent loops of order 2q, q a prime), or lead to efficient classification Computer programs. This allows Lis to enumerate all nilpotent loops of order less than 24. (C) 2009 Published by Elsevier Inc.