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Minimal Counterexamples to the Hall-Paige Conjecturethat any minimal counterexample must be “close” to being a simple group. In 1992 Evans tried to improve on this by extending complete mappings of ., a subgroup of . of index 2, to complete mappings of .; and complete mappings of .∕., ., to complete mappings of .. Evans’ proofs require that certain t替代品 发表于 2025-3-23 03:31:10
A Proof of the Hall-Paige Conjecture finite simple group of Lie type, with the possible exception of.(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 Gavi薄荷醇 发表于 2025-3-23 07:51:10
Orthomorphism Graphs of Groupsphism graphs: graphs whose vertices are orthomorphisms, and in which adjacency implies orthogonality. In this chapter we introduce orthomorphism graphs of groups. We describe the main problems of interest in the study of orthomorphism graphs, and we describe automorphisms and congruences of orthomor