On left distributive left quasigroups
by
David Stanovsky
Charles University in Prague

We establish a strong connection between finite left symetric left distributive idempotent quasigroups (i.e. those satisfying x(xy)=y, x(yz)=(xy)(xz) and xx=x) and Bruck loops of odd order (i.e. those satisfying the Bol identity and AIP). It allows to transfer many interesting properties proven for either of the structures earlier, such as solvability or the Lagrange property.

If time permits, we would like to present a description of all non-idempotent subdirectly irreducible left distributive left quasigroups.

Date received: May 11, 2004