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

• Author(s): Moses K. Maraka ; John W. Matuya ; Edward M. Njuguna ; Lewis N. Nyaga
• Paper ID: 1706002
• Page: 612-619
• Published Date: 14-09-2024
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 8 Issue 1 July-2024

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.

Citations

IRE Journals:
Moses K. Maraka , John W. Matuya , Edward M. Njuguna , Lewis N. Nyaga "Transitivity of the Product Action of Finite Alternating Groups on Cartesian Product of Finite Ordered Sets of Y-tuples" Iconic Research And Engineering Journals Volume 8 Issue 1 2024 Page 612-619

IEEE:
Moses K. Maraka , John W. Matuya , Edward M. Njuguna , Lewis N. Nyaga "Transitivity of the Product Action of Finite Alternating Groups on Cartesian Product of Finite Ordered Sets of Y-tuples" Iconic Research And Engineering Journals, 8(1)