(science publishing group, 2017-02) Gikunju, David Muriuki; Nyaga, Lewis Namu; Rimberia, Jane Kagwiria
Transitivity and Primitivity of the action of the direct product of the symmetric group on Cartesian product of
three sets are investigated in this paper. We prove that this action is both transitive and imprimitive for all n ³ 2 . In addition,
we establish that the rank associated with the action is a constant 3 2 .
Further; we calculate the subdegrees associated with the
action and arrange them according to their increasing magnitude.