Intersection theorems in permutation groups

The Hamming distance between two permutations of a finite set X is the number of elements of X on which they differ. In the first part of this paper, we consider bounds for the cardinality of a subset (or subgroup) of a permutation group P on X with prescribed distances between its elements. In the second part. We consider similar results for sets of s-tuples of permutations; the role of Hamming distance is played by the number of elements of X on which, for some i, the ith permutations of the two tuples differ.