Cycle type in Hall–Paige: a proof of the Friedlander–Gordon–Tannenbaum conjecture
Abstract
Abstract An orthomorphism of a finite group G is a bijection $\phi \colon G\to G$ such that $g\mapsto g^{-1}\phi (g)$ is also a bijection. In 1981, Friedlander, Gordon, and Tannenbaum conjectured that when G is abelian, for any $k\geq 2$ dividing $|G|-1$ , there exists an orthomorphism of G fixing the identity and permuting the remaining elements as products of disjoint k -cycles as long as the Sylow $2$ -subgroups of G are trivial or noncyclic. We prove this conjecture for all sufficiently large groups.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Combinatorial Mathematics
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Forum of Mathematics Sigma
- Publisher
- Cambridge University Press (CUP)
- Volume
- 14
- Publication date
- 1 January 2026
- Language
- EN