Transitivity of the Product Action of Finite Alternating Groups on Cartesian Product of Finite Ordered Sets of Y-tuples

References

[1] Cameron P.J. (1972). Permutation groups with multiply transitive suborbits. I. Proc. London Math. Soc. 23(30):427-440.

[2] Cameron P.J. (1973). Permutation groups with most suborbits doubly transitive. Geometriae Dedicata, 1(4),434-446.

[3] Hamma, S., & Aliyu, S. O. (2010). On transitive and primitive dihedral groups of degree 2r (r≥s2). Archives of Applied Science Research, 2(5), 152-160.

[4] Higman, D. G. (1964). Finite permutation groups of rank 3. Math Zeitschriff, 86:145– 156.

[5] Lopes, P. (2009). Permutations which make transitive groups primitive. Central European Journal of Mathematics (Cent. Eur. J. Math.), Vol7(4).650-659.

[6] Maraka K. Moses, Musundi W. Sammy, Lewis N. Nyaga, “Transitivity Action of the Cartesian Product of the Alternating Group Acting on a Cartesian Product of Ordered Sets of Triples”. Asian Research Journal of Mathematics (ARJOM), Vol. 17(12): 53-62, 2021.

[7] Maraka K. Moses, Musundi W. Sammy, Lewis N. Nyaga, “Primitivity Action of the Cartesian Product of an Alternating Group Acting on a Cartesian Product of Ordered Sets of Triples”. London Journals Press, Vol. 22(7): 25-32, 2022.

[8] Mutua, A.K., Nyaga, L.N. and Gachimu, R.K. (2018). Combinatorial properties, invariants and structures of the action of on . International Journal of Sciences: Basic and Applied Research (IJSBAR),Volume 40, No. 2, pp 109-115.

[9] Ndarinyo, C.W. and Rimberia, J.K. (2015). Transitivity Action of (𝑛=5,6,7) on Unordered and Ordered Triples. IJMSE 6(7), 21-27.

[10] Njagi, L.K. (2016). Ranks, subdegrees and suborbital graphs of symmetric group acting on ordered pairs. Journal of advance research in applied science (issn: 2208-2352), 3(2), 51-70.

[11] Nyaga, L. N. (2018). Transitivity of the direct product of the Alternating group acting on the cartesian product of three sets. International journal of mathematics and its applications (issn:2347-1557), rn, 55, 7.

[12] Rose, J. S. (1978). A course in group theory. Cambridge University Press, Cambridge.

@article{1706002,
      author = {Moses K. Maraka, John W. Matuya, Edward M. Njuguna, Lewis N. Nyaga},
      title = {Transitivity of the Product Action of Finite Alternating Groups on Cartesian Product of Finite Ordered Sets of Y-tuples},
      journal = {Iconic Research And Engineering Journals},
      year = {2024},
      volume = {8},
      number = {1},
      pages = {612-619},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1706002.pdf},
      abstract = {In this paper, we determine the transitivity of the product action of finite alternating groups on the Cartesian product of finite ordered sets of  ?-tuples. Transitivity action has been determined using the Orbit-stabilizer theorem, by showing that the length of the orbit (p_1,p_2,p_3,?,p_(m-1),p_m ) in  A_(n_1 )?A_(n_2 )ׅ?A_(n_(m-1) )?A_(n_m ),  (n-??2)  acting on  ?P_1?^[?] ??P_2?^[?] ׅ??P_(m-1)?^[?] ??P_m?^[?]   is equivalent to the cardinality of  ?P_1?^[?] ??P_2?^[?] ׅ??P_(m-1)?^[?] ??P_m?^[?]  to imply transitivity.},
      keywords = {Orbits; stabilizer; transitive group; ordered sets of ?-tuples; cartesian product; fixed point.},
      month = {July},
  }