### A classification of finite homogeneous semilinear spaces.

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In an absolute space $(P,\U0001d50f,\equiv ,\alpha )$ with congruence there are line reflections and point reflections. With the help of point reflections one can define in a natural way an addition + of points which is only associative if the product of three point reflection is a point reflection again. In general, for example for the case that $(P,\U0001d50f,\alpha )$ is a linear space with hyperbolic incidence structure, the addition is not associative. $(P,+)$ is a K-loop or a Bruck loop.

2000 Mathematics Subject Classification: 51E14, 51E30.We propose a method of constructing partial Steiner triple system, which generalizes the representation of the Desargues configuration as a suitable completion of three Veblen configurations. Some classification of the resulting configurations is given and the automorphism groups of configurations of several types are determined.

A quasiregular comfiguration is a finite partial plane, which not contains proper closed configuration. In this paper the authors investigate a representations of quasiregular configurations in real projective space and in comples projective plane.