## IP Loops of Small Order## Asif Ali and John Slaney
## DefinitionAn IP loop is a groupoid(L,*) such that
* is left and right cancellative: for all *x, y*in*L*there exist unique*z*in_{1}, z_{2}*L*such that*x*z*._{1}= y = z_{2}*xThere is an element *e*in*L*such that for all*x*in*L**e*x = x = x*e*;For every element *x*there is some element*x*such that for every*y*we have*x***(x*y) = y = (y*x)***x*.
A group is an associative IP loop. A Steiner loop is an IP loop in which for
every
## Small IP loopsClick on the following links to download the IP loops of order up to 13. One representative of each isomorphism class is given, in (numerical) lexicographic order.
Computer Sciences Laboratory, Australian National University |