The admissibility of sporadic simple groups
By Anthony B. Evans. 2009
61 citations recorded by the source corpus.
Abstract In 1955 Hall and Paige conjectured that a finite group is admissible, i.e., admits complete mappings, if its Sylow 2-subgroup is trivial or noncyclic. In a recent paper, Wilcox proved that any minimal counterexample to this conjecture must be simple, and further, must be either the Tits group or a sporadic simple group. In this paper we improve on this result by proving that the fourth Janko group is the only possible minimal counterexample to this conjecture: John Bray reports having proved that this group is also not a counterexample, thus completing a proof of the Hall–Paige conjecture.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/dfe0b6648bc8195c12398e4949a6a66565de3988
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In Algebra and Number Theory
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Citations in the corpus
- Transversals in Latin Squares (2009, background): “Evans [58] then showed that the only possible counterexample was Janko’s group J4.”
- Reduction of the Hall–Paige conjecture to sporadic simple groups (2009, background): “ contain a central involution [6]. Continuing in this direction, we will show that a minimal counterexample must be one of the 26 sporadic simple groups or the Tits group. In a companion paper, Evans [9] deals with 26 of these groups (including an alternative treatment of the Mathieu groups), leavin”