Ranks, Subdegrees and Suborbital Graphs of Direct Product of the Symmetric Group Acting on the Cartesian Product of Three Sets
Pure and Applied Mathematics Journal
Volume 6, Issue 1, February 2017, Pages: 1-4
Received: Dec. 17, 2016; Accepted: Jan. 3, 2017; Published: Feb. 2, 2017
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Authors
Gikunju David Muriuki, Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Nyaga Lewis Namu, Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Rimberia Jane Kagwiria, Department of Pure and Applied Sciences, Kenyatta University, Nairobi, Kenya
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Abstract
Transitivity and Primitivity of the action of the direct product of the symmetric group on Cartesian product of three sets are investigated in this paper. We prove that this action is both transitive and imprimitive for all n ≥ 2. In addition, we establish that the rank associated with the action is a constant 23 Further; we calculate the subdegrees associated with the action and arrange them according to their increasing magnitude.
Keywords
Direct Product, Symmetric Group, Action, Rank, Subdegrees, Cartesian Product, Suborbit
To cite this article
Gikunju David Muriuki, Nyaga Lewis Namu, Rimberia Jane Kagwiria, Ranks, Subdegrees and Suborbital Graphs of Direct Product of the Symmetric Group Acting on the Cartesian Product of Three Sets, Pure and Applied Mathematics Journal. Vol. 6, No. 1, 2017, pp. 1-4. doi: 10.11648/j.pamj.20170601.11
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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