Volume 1, Issue 1, December 2016, Page: 15-19
The Theorem of Cayley and Γ Matrices
Xiao-Yan Gu, Department of Physics, East China University of Science and Technology, Shanghai, China
Jian-Qiang Sun, College of Information Science and Technology, Hainan University, Haikou, China
Received: Oct. 31, 2016;       Accepted: Nov. 17, 2016;       Published: Dec. 27, 2016
DOI: 10.11648/j.dmath.20160101.13      View  2695      Downloads  111
Abstract
In this article, the connections between symmetric groups and the matrix groups are investigated for exploring the application of Cayley’s theorem in finite group theory. The exact forms of the permutation groups isomorphic to the groups , and are obtained within the frame of the group-theoretical approach. The results are analyzed in detail and compared with that from Cayley's theorem. It shows that the orders of the symmetric groups in present formulas are less than the latter. Various directions for future investigations on the research results have been pointed out.
Keywords
Permutation Group, Isomorphic, γ Matrices, Cayley's Theorem, Quaternion Group
To cite this article
Xiao-Yan Gu, Jian-Qiang Sun, The Theorem of Cayley and Γ Matrices, International Journal of Discrete Mathematics. Vol. 1, No. 1, 2016, pp. 15-19. doi: 10.11648/j.dmath.20160101.13
Copyright
Copyright © 2016 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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