Lateinische Quadrate, ihre Geometrien und ihre Gruppen. (Latin squares, their geometries and groups.). (German) Zbl 0581.05014

This article is a comprehensive presentation of a talk the author gave to the 1983 DMV-Meeting in Cologne. The author is mainly concerned with what finite geometry is and what are its roots. He mentions finite affine and projective structures, block designs, transformation groups, and more recent interaction with the fields of information theory and data processing. He covers Latin squares, quasigroups, orthogonal arrays, existence theorems for Latin squares, construction methods for Latin squares and for block designs, completion, geometric configurations, like loops and nets, translation nets, groups on them. He concludes with an outlook upon open problems. The bibliography contains 132 items and is helpful in getting closer into the fields mentioned.
Reviewer: H.Kröger


05B15 Orthogonal arrays, Latin squares, Room squares
05B25 Combinatorial aspects of finite geometries
05-02 Research exposition (monographs, survey articles) pertaining to combinatorics