The Hall-Paige conjecture, and synchronization for affine and diagonal groups

DOI10.1016/j.jalgebra.2019.02.025zbMath1485.20002arXiv1811.12671OpenAlexW2902928475WikidataQ122956391 ScholiaQ122956391MaRDI QIDQ2282980

Hua Zhang, Pablo Spiga, Qi Cai, Peter J. Cameron, John N. Bray

Publication date: 27 December 2019

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.12671

zbMATH Keywords

automatagraphsprimitive groupsHall-Paige conjecturetransformation semigroupscomplete mappingsorbitalssynchronizing groupsseparating groups

Mathematics Subject Classification ID

Semigroups of transformations, relations, partitions, etc. (20M20) Association schemes, strongly regular graphs (05E30) Simple groups: sporadic groups (20D08) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Semigroups in automata theory, linguistics, etc. (20M35) Primitive groups (20B15)

Related Items (19)

Transversals, near transversals, and diagonals in iterated groups and quasigroups ⋮ Diagonal groups and arcs over groups ⋮ Coset-wise affine functions and cycle types of complete mappings ⋮ Cycle types of complete mappings of finite fields ⋮ The geometry of diagonal groups ⋮ Synchronising primitive groups of diagonal type exist ⋮ Difference matrices with four rows over generalized dihedral groups ⋮ Combinatorics, probability and computing. Abstracts from the workshop held April 24--30, 2022 ⋮ Separating rank 3 graphs ⋮ Compositions and parities of complete mappings and of orthomorphisms ⋮ Partial orthomorphisms and Latin squares based on parts of a group ⋮ Computational group theory. Abstracts from the workshop held August 15--21, 2021 (hybrid meeting) ⋮ The diagonal graph ⋮ The Bruhat order on classes of isotopic Latin squares ⋮ Latin squares with maximal partial transversals of many lengths ⋮ Strong complete mappings for 3-groups ⋮ Finite groups with an automorphism that is a complete mapping ⋮ A note on a pair of orthogonal orthomorphisms of cyclic groups ⋮ Difference matrices with five rows over finite abelian groups

Uses Software

• GAP
• Magma
• ATLAS Group Representations

Cites Work

• Unnamed Item
• Reduction of the Hall-Paige conjecture to sporadic simple groups.
• The Magma algebra system. I: The user language
• An improved method for generating the centralizer of an involution
• Between primitive and 2-transitive: synchronization and its friends
• Synchronization and separation in the Johnson schemes
• On ovoids of parabolic quadrics
• The admissibility of sporadic simple groups.
• The Maximal Subgroups of J ₄
• Permutation Groups and Cartesian Decompositions
• The geometry of diagonal groups
• Complete mappings of finite groups

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