Reduction of the Hall–Paige conjecture to sporadic simple groups
By Stewart Wilcox. 2009
60 citations recorded by the source corpus.
Abstract A complete mapping of a group G is a permutation ϕ : G → G such that g ↦ g ϕ ( g ) is also a permutation. Complete mappings of G are equivalent to transversals of the Cayley table of G, considered as a Latin square. In 1953, Hall and Paige proved that a finite group admits a complete mapping only if its Sylow-2 subgroup is trivial or noncyclic. They conjectured that this condition is also sufficient. We prove that it is sufficient to check the conjecture for the 26 sporadic simple groups and the Tits group.
Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/307578c228a4749b1a12ea729c84b4193cd72029
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In Artificial Intelligence
In Discrete Mathematics and Combinatorics
In Electrical and Electronic Engineering
Citations in the corpus
- Transversals in Latin Squares (2009, background): “In a preprint Wilcox [58] has claimed to reduce the problem to showing it for the sporadic simple groups (of which the Mathieu groups have already been handled in [13]).”