Bol quasifields

Abstract

In the context of configurational characterisations of symmetric projective planes, a new proof of a theorem of Kallaher and Ostrom characterising planes of even order of Lenz-Barlotti type IV.a.2 via Bol conditions is given. In contrast to their proof, we need neither the Feit-Thompson theorem on solubility of groups of odd order, nor Bender's strongly embedded subgroup theorem, depending rather on Glauberman's $Z^*$-theorem.