Application of Group Theory to the Analysis of Symmetry Problems

Mathematics — 2025, Undergraduate

This study examined the application of group theory to the analysis of symmetry problems. Symmetry groups were constructed for selected geometric and physical configurations and analysed using group axioms, subgroups, and cosets. The findings revealed that group-theoretic descriptions captured the structure of symmetries compactly and supported classification of configurations by symmetry type. The study observed that the group framework simplified analysis of combined transformations. It recommends the continued application of group methods in geometry, crystallography, and physics.

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