Generalization of infinite groups

Yuting Dai; Weizhe Huang; Xintong Ji; Minghan Jia

doi:10.1117/12.2685932

28 July 2023 Generalization of infinite groups

Yuting Dai, Weizhe Huang, Xintong Ji, Minghan Jia

Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 1275603 (2023) https://doi.org/10.1117/12.2685932
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China

Abstract

Nowadays many different physical structures, such as crystal structure and hydrogen atom structure, can be modelled using group theory methods. This paper mainly focuses on four aspects: infinite groups in general, the irrecognizable infinite groups, cosets of infinite groups, Sylow’s theorems and the Sylow tower group. In this research, different fundamental aspects of group theory in linear algebra and their applications in both finite and infinite groups are explored. The definition and examples of groups are first given, and the irrecognizable infinite group is then introduced. In addition, the concept of cosets of infinite groups is explained with the definition of subgroups, especially normal subgroups, as well as the Lagrange’s theorem. Lastly, Sylow’s first, second and third theorems, and the properties of Sylow tower group are also demonstrated. Therefore, readers are able to use the knowledge of groups to analyse symmetric mathematical phenomena since group theory can be described as a study of symmetry.

Citation Download Citation

Yuting Dai, Weizhe Huang, Xintong Ji, and Minghan Jia "Generalization of infinite groups", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 1275603 (28 July 2023); https://doi.org/10.1117/12.2685932

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