The Imprimitivity Action of the Product of Finite Alternating Groups on Cartesian Product of Ordered γ- Tuples of Finite Sets
Moses Khakame Maraka, John Wanyonyi Matuya, Edward M. Njuguna, Lewis N. Nyaga · 2025
A group G acts primitively on a set P if the only G -invariant partitions are trivial. This paper explores the primitivity of the product action of finite alternating groups An1×An2× …×Anm on the Cartesian product of finite sets of ordered y -tuples. We demonstrate that for all n-γ≥2, this action is imprimitive by constructing explicit non-trivial block systems. This finding adds to previous research on the transitivity of such actions.