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A Class of Homomorphisms of Pre-Hjelmslev Groups

Published online by Cambridge University Press:  20 November 2018

Frieder Knüppel
Frieder Knüppel*
Affiliation:
Universität Kiel, Kiel, W. Germany
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E. Salow [8] introduced the concept of pre-Hjelmslev groups, a generalization of F. Bachmann's Hjelmslev groups [1] which leads to a more natural theory of homomorphisms and permits a simpler construction of algebraic models. Basically, both types of groups are the groups of motions of a metric plane, the so-called group plane. In such a plane there is a unique perpendicular through any point to any line and the product of three collinear points (three copunctal lines) is a point (a line). Our first section contains the precise definitions and some basic facts.

The homomorphic image of a pre-Hjelmslev group can be more complicated than the pre-image. For instance, there may always be a unique line through two distinct points of the pre-image but not of the image. We study regular homomorphisms of pre-Hjelmslev groups, i.e., homomorphisms with the following property: If two lines intersect at exactly one point, their images will also have precisely one point in common.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 3 , 01 June 1984 , pp. 470 - 494
Copyright
Copyright © Canadian Mathematical Society 1984

References

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