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Research on Group Actions and Related Theorems

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This dissertation examines group actions, highlighting the orbit-stabilizer theorem and its implications in mathematics.

Group action serves as a valuable framework for examining the symmetries of mathematical structures, providing insights into their properties and transformations.
The orbit-stabilizer theorem illustrates crucial concepts such as orbit and stabilizer, facilitating a deeper understanding of equivalence relations on sets.
This research reinforces the theoretical foundations of group actions by proving several related theorems that aid in the comprehension of these mathematical concepts.
Connections to geometry, topology, and number theory demonstrate the interdisciplinary nature of group action and its broad applications in mathematics.

Mingyue Sun (2025) studied this question.

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