Doubly transitive 2‐factorizations

Let $\cal F$ be a 2‐factorization of the complete graph K v admitting an automorphism group G acting doubly transitively on the set of vertices. The vertex‐set V ( K v ) can then be identified with the point‐set of AG ( n, p ) and each 2‐factor of $\cal F$ is the union of p ‐cycles which are obtained from a parallel class of lines of AG ( n, p ) in a suitable manner, the group G being a subgroup of A G L ( n, p ) in this case. The proof relies on the classification of 2‐( v, k , 1) designs admitting a doubly transitive automorphism group. The same conclusion holds even if G is only assumed to act doubly homogeneously. © 2006 Wiley Periodicals, Inc. J Combin Designs