Action of Direct Products of Four Alternating Groups on Cartesian Product of Four Sets

Abstract

In this paper, transitivity, primitivity, ranks and subdegrees associated with the action of direct product of four Alternating groups An, where n is a positive integer atleast 2 on the Cartesian product of four sets are investigated. It is shown that for n > 2, the action is both transitive and imprimitive. It is further shown that the rank associated with this action is a constant of 16 and the ........

Keywords: Alternating Group, Transitivity, Primitivity, Ranks, Subdegrees, Direct Product, Cartesian Product, GAP