Presented by: 
Thomas McCourt, Plymouth University
Tue 7 Jun, 3:00 pm - 4:00 pm

The Axiom of Veblen (or Veblen-Youngs Axiom) is one of the axioms that defines projective spaces. In the case of finite geometries where lines have size three it gives rise to the Projective Steiner triple systems. In turn Steiner triple systems are equivalent to quasigroups that satisfy certain algebraic conditions. Using these equivalences the Axiom of Veblen can be interpreted as an algebraic condition. In this talk we will consider a generalisation of this algebraic condition, namely we ‘throw away’ commutativity. In many cases commutativity comes back as a consequence of other conditions, but not in all cases…