The structures of the subgroups play an important role in the study of the nature of symmetric groups. We calculate the 11300 subgroups of the permutation group S7 by group-theoretical approach. The analytic expressions for the numbers of subgroups are obtained. The subgroups of the permutation group S7 are all represented in an alternative way for further analysis and applications.
| Published in | International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 1) |
| DOI | 10.11648/j.ijtam.20170301.13 |
| Page(s) | 19-24 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Permutation Group, Subgroup, Lagrange’s Theorem, Cayley’s Theorem
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APA Style
Xiao-Yan Gu, Jian-Qiang Sun. (2016). Analysis on the Properties of a Permutation Group. International Journal of Theoretical and Applied Mathematics, 3(1), 19-24. https://doi.org/10.11648/j.ijtam.20170301.13
ACS Style
Xiao-Yan Gu; Jian-Qiang Sun. Analysis on the Properties of a Permutation Group. Int. J. Theor. Appl. Math. 2016, 3(1), 19-24. doi: 10.11648/j.ijtam.20170301.13
AMA Style
Xiao-Yan Gu, Jian-Qiang Sun. Analysis on the Properties of a Permutation Group. Int J Theor Appl Math. 2016;3(1):19-24. doi: 10.11648/j.ijtam.20170301.13
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Download@article{10.11648/j.ijtam.20170301.13,
author = {Xiao-Yan Gu and Jian-Qiang Sun},
title = {Analysis on the Properties of a Permutation Group},
journal = {International Journal of Theoretical and Applied Mathematics},
volume = {3},
number = {1},
pages = {19-24},
doi = {10.11648/j.ijtam.20170301.13},
url = {https://doi.org/10.11648/j.ijtam.20170301.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170301.13},
abstract = {The structures of the subgroups play an important role in the study of the nature of symmetric groups. We calculate the 11300 subgroups of the permutation group S7 by group-theoretical approach. The analytic expressions for the numbers of subgroups are obtained. The subgroups of the permutation group S7 are all represented in an alternative way for further analysis and applications.},
year = {2016}
}
TY - JOUR T1 - Analysis on the Properties of a Permutation Group AU - Xiao-Yan Gu AU - Jian-Qiang Sun Y1 - 2016/12/27 PY - 2016 N1 - https://doi.org/10.11648/j.ijtam.20170301.13 DO - 10.11648/j.ijtam.20170301.13 T2 - International Journal of Theoretical and Applied Mathematics JF - International Journal of Theoretical and Applied Mathematics JO - International Journal of Theoretical and Applied Mathematics SP - 19 EP - 24 PB - Science Publishing Group SN - 2575-5080 UR - https://doi.org/10.11648/j.ijtam.20170301.13 AB - The structures of the subgroups play an important role in the study of the nature of symmetric groups. We calculate the 11300 subgroups of the permutation group S7 by group-theoretical approach. The analytic expressions for the numbers of subgroups are obtained. The subgroups of the permutation group S7 are all represented in an alternative way for further analysis and applications. VL - 3 IS - 1 ER -
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