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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.
Complete mappings of finite groups
M. Hall and L. Paige · 1955
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Sorting networks and their applications
K. E. Batcher · 1968
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On sums of integers taken from a fixed sequence
R. Graham · 1971
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Combinatorial structures in loops I. elements of the decomposition theory
E. C. Johnsen and T. Storer · 1973
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Cyclic arrangements of the elements of a group
G. Ringel · 1974
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On a group sequencing problem of Ringel
R. J. Friedlander, B. Gordon, and M. D. Miller · 1978
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Partitions of groups and complete mappings
R. Friedlander, B. Gordon, and P. Tannenbaum · 1981
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Sorting in c log n c\log n parallel steps
M. Ajtai, J. Komlós, and E. Szemerédi · 1983
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