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An asymptotic for the Hall–Paige conjecture by Sean Eberhard; Freddie Manners; Rudi Mrazović is a Mathematics article available to read on EtoBox.

What is An asymptotic for the Hall–Paige conjecture about?

Hall and Paige conjectured in 1955 that a finite group G has a complete mapping if and only if its Sylow 2subgroups are trivial or noncyclic. This conjecture was proved in 2009 by Wilcox, Evans, and Bray using the classification of finite simple groups and extensive computer algebra. Using a completely different approach motivated by the circle method from analytic number theory, we prove that the number of complete mappings of any group G of order n satisfying the Hall-Paige condition is (e -1/2 + o(1)) |G ab | n! 2 /n n .

Who reads An asymptotic for the Hall–Paige conjecture?

Author

Sean Eberhard; Freddie Manners; Rudi Mrazović

Publisher

Elsevier BV

Published

2022

Language

EN

Field

Mathematics (Physical Sciences)