Ranks and Subdegrees of the Action of the Product of Three Alternating Groups on the Cartesian Product of Three Sets of Ordered γ-Tuples
Moses K. Maraka *
Department of Mathematics & Physical Sciences, Maasai Mara University; P.O. Box 861-20500, Narok, Kenya.
John W. Matuya
Department of Mathematics & Physical Sciences, Maasai Mara University; P.O. Box 861-20500, Narok, Kenya.
Edward M. Njuguna
Department of Mathematics & Physical Sciences, Maasai Mara University; P.O. Box 861-20500, Narok, Kenya.
Lewis N. Nyaga
Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology; P.O. Box 62000-00200 Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the ranks and subdegrees of the action of the product of three alternating groups, An1×An2×An3, acting on the Cartesian product of three sets of ordered γ –tuples, P1[γ] × P2[γ] × P3[γ], are determined. Using combinatorial formula and mathematical induction, ∀ n - γ ≥ 2, the rank of An1 × An2 × An3 acting on P1[γ] × P2[γ] × P3[γ] is and the subdegrees of An1 × An2 × An3, on P1[γ] × P2[γ] × P3[γ] are: 1,
Keywords: Group action, cartesian product, rank and subdegrees