Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Proceedings of the 2nd International Conference on Computing Innovation and Applied Physics (CONF-CIAP 2023)
Series Vol. 5 , 25 May 2023
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The Rubik’s Cubes in Group Theory
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Abstract
This paper expounds the basic concept of group theory and its application in Rubik’s Cube transformation and restoration formula. The different states of the magic cube are regarded as the elements of the magic cube group, and the set generated by six basic operations is equivalent to the homomorphism of the magic cube group for analysis, from the mathematical characteristics of the permutation group to some practical examples. The collection of possible states of Rubik's Cube is a group, called Rubik's Cube Group, which can be analyzed with the knowledge of group theory. The essence of the magic cube group is the subgroup of the substitution group. There are six basic operations of the magic cube. The combination of basic operations can only produce even pairs of blocks to exchange positions or flip directions at the same time. Therefore, there are some restrictions on the transformation of the magic cube. Some practical examples give some ideas for creating the magic cube formula.
Keywords
Group theory, Permutation group, Homomorphism, Rubik’s Cubes.
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 2nd International Conference on Computing Innovation and Applied Physics (CONF-CIAP 2023)
- ISBN (Print)
- 978-1-915371-53-9
- ISBN (Online)
- 978-1-915371-54-6
- Published Date
- 25 May 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/5/20230454
- Copyright
- © 2023 The Author(s)
- 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