The transitivity of Conway's [formula omitted

Abstract

J.H. Conway introduced a set of permutations called M 13 by a game related to the projective plane of order 3. The set M 13 consists of certain permutations on 13 letters, and contains the Mathieu group M 12 . W.J. Martin and B.E. Sagan generalized the concept of transitivity for a set of permutations by defining λ -transitivity for each partition λ of the degree of the permutations. We determine the partitions λ of 13 for which the set M 13 is λ -transitive.