TRANSITIVITY, RANK, AND SUBORBITSOF THE CYCLIC GROUP Cn ACTING ON UNORDERED SUBSETS

Abstract

The study aims at determining the rank and subdegrees of the cyclic group, C n = <(12…n)> acting on X (r) , the set of unordered subsets of X={1, 2, …, n}. It has been shown that the action of C n on X (r) is transitive if and only ifr=1, r=n-1 orr=n. The rankfor transitive actions has been shown to ben. The number of self paired suborbits has been computed and conditions for paired suborbits discussed. The results have shown that the action of C n on X is equivalent to that of C n onX (n-1) .