Action of the Symmetric Group \(S_7\) on Unordered Pairs
Stanley K. Rotich *
Department of Mathematics, Statistics and Actuarial Science, Machakos University, P.O. Box 136, Machakos, Kenya.
*Author to whom correspondence should be addressed.
Abstract
In this paper some properties of Symmetric group G = \(S_7\) on \(X^2\) are investigated. It is shown that G acts transitively, primitively but not doubly transitively on \(X^2\) . The orbits of G {1,2} acting on \(X^2\) and the orbits of G acting on \(X^2\) \(\times\) \(X^2\) are found to be 3. Suborbital graphs corresponding to the action of G on \(X^2\) \(\times\) \(X^2\) are constructed. Some theoretic properties of these graphs are discussed.
Keywords: Transitive, orbits, suborbits, suborbital graphs