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Applications of complete mappings and orthomorphisms of finite groups. (English) Zbl 1328.05026

This is a survey paper, which shows how complete mappings and orthomorphisms have been used to obtain certain results related to various combinatorial and algebraic structures. These include (1) constructions of certain types of mutually orthogonal Latin squares and Latin squares with certain properties (2) establishing existence of certain types of sequencings of the elements in a finite group and (3) certain results related to neofields.

MSC:

05B15 Orthogonal arrays, Latin squares, Room squares
20D60 Arithmetic and combinatorial problems involving abstract finite groups
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