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Volume 9, Issue 6, December 2020, Page: 175-178
A Construction of Imprimitive Groups of Rank 4 or 5
Chang Wang, School of Mathematics, Yunnan Normal University, Kunming, China
Renbing Xiao, School of Mathematics, Yunnan Normal University, Kunming, China
Received: Sep. 15, 2020;       Accepted: Oct. 23, 2020;       Published: Nov. 4, 2020
DOI: 10.11648/j.acm.20200906.11      View  52      Downloads  22
Abstract
Let G be a transitive permutation group acting on a finite set Ω. For a point α of Ω, the set of the images of G acting on α is called the orbit of α under G and is denoted by αG, and the set of elements in G which fix α is called the stabilizer of α in G and is denoted by Gα. We can get some new orbits by using the natural action of the stabilizer Gα on Ω, and then we can define the suborbit of G. The suborbits of G on Ω are defined as the orbits of a point stabilizer on Ω. The number of suborbits is called the rank of G and the length of suborbits is called the subdegree of G. For finite primitive groups, the study of the rank and subdegrees of group has a long history. In this paper, we construct a class of imprimitive permutation groups of rank 4 or 5 by using imprimitive action and product action of wreath product, determine the number and the length of the suborbits, and extend the results to imprimitive permutation groups of rank m+1 and 2n+1, where m and n are positive integers.
Keywords
Permutation Group, Transitive Action, Rank, Suborbit
To cite this article
Chang Wang, Renbing Xiao, A Construction of Imprimitive Groups of Rank 4 or 5, Applied and Computational Mathematics. Vol. 9, No. 6, 2020, pp. 175-178. doi: 10.11648/j.acm.20200906.11
Copyright
Copyright © 2020 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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