Frobenius Quasigroups and Regular Polygons

被引：0

作者：

Iden O. ^{[1
]}

Strambach K. ^{[2
]}

机构：

[1] Department of Mathematics, University of Bergen, Johannes Brunsgate 12, Bergen

[2] Mathematisches Institut, Universität Erlangen, Bismarckstr. 1 1/2, Erlangen

来源：

Results in Mathematics | 2004年 / 45卷 / 3-4期

关键词：

algebraic and topological quasigroups; Frobenius groups; left distributive quasigroups;

D O I：

10.1007/BF03323381

中图分类号：

学科分类号：

摘要：

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. © 2004, Birkhäuser Verlag, Basel.

引用

页码：254 / 273

页数：19

共 22 条

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