Commutative loops of exponent two and involutorial 3-nets with identity
3-nets are one generalization of affine planes. To every quasigroup there corresponds a uniquely determined 3-net, and to every 3-net there corresponds a set of pairwise isostrophic quasigroups. In that sense, 3- nets are co-ordinatized by quasigroups. In this paper, the authors investigate 3-nets co-ordinatized by commutative loops of exponent two. The authors call them involutive 3-nets with identity. In particular, they consider direction-preserving collineation groups which stabilize the transversal line \(e_ t\) consisting of all points (x,x).
scientific article; zbMATH DE number 4114898