Permutation groups: factorisations, structure and applications

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Group theory is the mathematical study of symmetry. This project aims to improve our understanding of the structure of groups by studying their factorisations and the structure of certain subgroups and elements. The obtained knowledge will be applied to study embeddings of graphs on surfaces and regular subgroups of important families of groups. The main impact would be in areas of pure mathematics such as group theory and graph theory by strengthening our knowledge of the finite simple groups.