Abstract
In 2009 Wilcox proved that any minimal counterexample to the Hall-Paige conjecture must be a finite nonabelian simple group. He further proved that no finite simple group of Lie type, with the possible exception of2F4(2)′, the Tits group, could be a minimal counterexample to this conjecture. As the alternating groups were proved to be admissible in 1955 by Hall and Paige, and the Mathieu groups were proved admissible in 1993 by Dalla Volta and Gavioli, this left 22 possible minimal counterexamples to the Hall-Paige conjecture. Building on Wilcox’s work, Evans reduced the number of possible minimal counterexamples to the Hall-Paige conjecture to just one; Janko’s fourth group, J4. This last group was shown not to be a minimal counterexample by Bray, thus completing a proof of the conjecture. In this chapter we will cover proofs that finite nonabelian simple groups are admissible.
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Evans, A.B. (2018). A Proof of the Hall-Paige Conjecture. In: Orthogonal Latin Squares Based on Groups. Developments in Mathematics, vol 57. Springer, Cham. https://doi.org/10.1007/978-3-319-94430-2_7
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