September 12, 2008:

Petr Vojtechovsky, University of Denver 

Enumeration of nilpotent loops via cohomology


Abstract.  

The correspondence between central group extensions and 2-cocycles carries to the nonassociative case. By carefully investigating the coboundaries and the action of the automorphism group on the 2-cocycles, we classify centrally nilpotent loops of small orders with minimal usage of computers. We also obtain a formula for the number of nilpotent loops of order 2p and describe its asymptotic behavior. This is joint work with Dan Daly.