We discuss the general relationship between the number of orbits of the wreath product and the orbits of two permutation groups that constitute the wreath product. Examples are provided to illustrate the relationship.

wreath product, group action, finite permutation groups, symmetry groups, application of symmetry groups.

Received: September 19, 2023; Revised: October 3, 2023; Accepted: November 2, 2023

How to cite this article: Bashayer S. Alharbi and Ahmad M. Alghamdi, On orbits of wreath product of finite groups, JP Journal of Algebra, Number Theory and Applications 63(1) (2024), 23-54. http://dx.doi.org/10.17654/0972555524002

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