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Group Theory

Hall-Paige conjecture ★★★

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

Posted by mdevos
updated October 21st, 2007
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