A Representation of a Point Symmetric 2-Structure by a Quasi-Domain

In a symmetric 2-structure ${Sigma =(P,mathfrak{G}_1,mathfrak{G}_2,mathfrak{K})}$ we fix a chain ${E in mathfrak{K}}$ and define on E two binary operations “+” and “·”. Then (E,+) is a K-loop and for ${E^* := E {setminus}{o}}$ , (E ^*,·) is a Bol loop. If ${Sigma}$ is even point symmetric then (E,+ ,·) is a quasidomain and one has the set ${Aff(E,+,cdot) := {a^+circ b^bullet | a in E, b in E^*}}$ of affine permutations. From Aff(E, +, ·) one can reproduce via a “chain derivation” the point symmetric 2-structure ${Sigma}$ .