Efficient Computation in Finite Groups

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This project will investigate efficient manipulation of finite groups and estimation of their parameters. The main focus is on the design and analysis of efficient algorithms for large group-theoretic problems. While interested in improved asymptotic performance, the project will also emphasize practicability, demonstrating the relevance of the asymptotic paradigm to efficient implementation. Of interest also is the development of parallel versions of the algorithms. The investigation will be extended to matrix groups, the most frequently occurring representations of finite groups. Finally, the project will investigate important parameters of groups, especially the estimation of diameters of various classes of Cayley graphs.