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Sequenceable groups and related topics. (English) Zbl 1081.20500

Summary: In 1980, about 20 years after sequenceable groups were introduced by Gordon to construct row-complete Latin squares, Keedwell published a survey of all the available results concerning sequencings. This was updated (jointly with Dénes) in 1991 and a short overview, including results about complete mappings and \(R\)-sequencings, was given in the CRC Handbook of Combinatorial Designs in 1995. In Sections 1 and 2 we give a survey of the current situation concerning sequencings. In Section 3 we consider some concepts closely related to sequenceable groups: terraces, \(R\)-sequencings, super sequenceable groups (also known as super \(P\)-groups) and the Gordon game. We also look at constructions for row-complete Latin squares that do not use sequencings.

MSC:

20D60 Arithmetic and combinatorial problems involving abstract finite groups
05B15 Orthogonal arrays, Latin squares, Room squares
20-02 Research exposition (monographs, survey articles) pertaining to group theory