Established results in group theory

Zihui Bao; Shiyang Hu; Kecen Zhou

doi:10.1117/12.2639420

17 May 2022 Established results in group theory

Zihui Bao, Shiyang Hu, Kecen Zhou

Proceedings Volume 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022); 1225918 (2022) https://doi.org/10.1117/12.2639420
Event: 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing, 2022, Kunming, China

Abstract

Group theory, as a part of abstract algebra, was originated from 19th century and keep reaching its peak since around 50 years ago. The important results were collaborative efforts from various mathematicians including Cauchy’s Theorem, Sylow’s Theorem and Lagrange’s Theorem, and these results put group theory in a significant place of algebra.This paper talks about both finite group actions and infinite group actions with definition and accessible examples. The paper then gives definition and explanation on stabilisers and orbits, also with their corresponding examples in order to provide the demonstration of the statement of Orbit-Stabiliser Theorem, after that, its proof follows. In the last part of this paper, we finally introduce the statement of Cauchy’s Theorem and present its proofs as understandable as possible.

Citation Download Citation

Zihui Bao, Shiyang Hu, and Kecen Zhou "Established results in group theory", Proc. SPIE 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), 1225918 (17 May 2022); https://doi.org/10.1117/12.2639420

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