Article

The structure of symmetry groups of almost perfect one factorizations

The concept of j-perfection of a one factorization is introduced. A one factorization is perfect if and only if it is 2-perfect. We call 3-perfect one factorizations almost perfect one-factorizations (or APOFs). First we give some general results concerning the automorphism groups of j-perfect one factorizations, and then we classify all APOFs which have more than one automorphism of order two with fixed points. Several structure theorems for the automorphism groups of APOFs are also given.

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