Abstract
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 \({\Sigma}\).
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Dedicated to Momme Thomsen on the occasion of his 70th birthday
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Karzel, H., Kosiorek, J. & Matraś, A. A Representation of a Point Symmetric 2-Structure by a Quasi-Domain. Results. Math. 65, 333–346 (2014). https://doi.org/10.1007/s00025-013-0348-0
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DOI: https://doi.org/10.1007/s00025-013-0348-0