Action of the Symmetric Group \(S_7\) on Unordered Pairs
Journal of Advances in Mathematics and Computer Science · pp. 36–46 · Published 21 Apr 2023
10.9734/jamcs/2023/v38i71770Abstract
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.
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