Theoretical analysis demonstrates transitive yet imprimitive actions of three alternating groups on ordered quadruples for n ≥ 6, highlighting structured symmetries in permutation groups.
In this paper, we determine the transitivity and primitivity of the product of three alternating groups acting on the cartesian product of three sets of ordered quadruples. When n ≥ 6 and using the Orbit-Stabilizer theorem, the action has been determined to be transitive and using the definition of primitivity and blocks, the action has been determined to be imprimitive.
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Moses K. Maraka (2026) studied this question.
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