Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 9, 13 November 2023
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Group action and its application on classification of low order groups
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Abstract
The classification of finite groups is an important topic in mathematics throughout history of mathematics. The topic of this paper is to use group action as a tool, to classify some special finite groups and some low order groups. First this paper introduces some concepts of group action. Then this paper states and proves some important theorems related to group action. For example, the Sylow’s theorem, which is very important in this paper. Research has found that, groups of specific order, such as groups whose order are 2p,p^2, pq(p, q are distinct prime numbers), p3(p is prime) can be classified using group action and the technique of semi-direct product, and groups whose order are no more than 15 are classified which can be seen as the special situations of the above ones. But in general, to make classification of a larger range of finite groups, more tools should be introduced.
Keywords
Finite Groups, Group Action, Sylow’s Theorem
References
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Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
- ISBN (Print)
- 978-1-83558-129-2
- ISBN (Online)
- 978-1-83558-130-8
- Published Date
- 13 November 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/9/20240733
- Copyright
- 13 November 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited