Results in Mathematics

, Volume 45, Issue 3–4, pp 254–273 | Cite as

Frobenius Quasigroups and Regular Polygons



In terms of regular n-gons a left distributive quasigroup operation is defined on the complex plane. This operation can be expressed by means of a semidirect product G of the translation group (which is sharply transitive on the points of the plane and hence may be identified with the plane) by a finite cyclic group of rotations of order n. That observation makes possible a wide generalization of this geometric quasigroup construction. The connection in general between algebraic properties of the quasigroup and various properties of the group G is discussed, in particular it is studied what the consequences for the quasigroup Q are if G is interpreted as a topological group or an algebraic group.

MSC Classification

20F29 20N10 22A30 14L99 51H20 51H30 

Key Words

Frobenius groups left distributive quasigroups algebraic and topological quasigroups 


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Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BergenBergenNorway
  2. 2.Mathematisches InstitutUniversität ErlangenErlangenGermany

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