Abstract
We have called a group admissible if it admits complete mappings and we proved that a finite group cannot be admissible if its Sylow 2-subgroup is nontrivial and cyclic. We proved the converse, known as the Hall-Paige conjecture, for abelian groups and groups of odd order. In this chapter we will prove the Hall-Paige conjecture true for more classes of groups. We will introduce HP-systems, an important tool in the construction of complete mappings, and use these to prove the Hall-Paige conjecture true for alternating and symmetric groups. We will also prove the Hall-Paige conjecture true for solvable groups, for Mathieu groups, for Suzuki groups, for certain unitary groups, and for groups whose Sylow 2-subgroups intersect trivially.
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Evans, A.B. (2018). Some Classes of Admissible Groups. In: Orthogonal Latin Squares Based on Groups. Developments in Mathematics, vol 57. Springer, Cham. https://doi.org/10.1007/978-3-319-94430-2_4
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DOI: https://doi.org/10.1007/978-3-319-94430-2_4
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