complete map

Hall-Paige conjecture โ˜…โ˜…โ˜…

Author(s): Hall; Paige

A complete map for a (multiplicative) group $ G $ is a bijection $ \phi : G \rightarrow G $ so that the map $ x \rightarrow x \phi (x) $ is also a bijection.

Conjecture   If $ G $ is a finite group and the Sylow 2-subgroups of $ G $ are either trivial or non-cyclic, then $ G $ has a complete map.

Keywords: complete map; finite group; latin square

Syndicate content