Transitivity Action of the Cartesian Product of the Alternating Group Acting on a Cartesian Product of Ordered Sets of Triples

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Date

2021

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Abstract

In this paper, we investigate some transitivity action properties of the cartesian product of the alternating group 𝐴𝑛(𝑛 ≥ 5) acting on a cartesian product of ordered sets of triples using the Orbit-Stabilizer Theorem by showing that the length of the orbit (𝑝, 𝑠, 𝑣) in 𝐴𝑛 × 𝐴𝑛 × 𝐴𝑛, (𝑛 ≥ 5) acting on 𝑃[3] × 𝑆[3] × 𝑉[3] is equivalent to the cardinality of 𝑃[3] × 𝑆[3] × 𝑉[3] to imply transitivity.

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Research Article

Keywords

Orbits, Stabilizer, Transitivity Action, Ordered Sets of Triples, Cartesian Product, Fixed Point.

Citation

Moses, M. K., Sammy, M. W., & Nyaga, L. N. (2021). Transitivity Action of the Cartesian Product of the Alternating Group Acting on a Cartesian Product of Ordered Sets of Triples.

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