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Geodetic groups: new advances in algebra and computer science

Project Member(s): Elder, M.

Funding or Partner Organisation: Australian Research Council (ARC Discovery Projects)
Australian Research Council (ARC Discovery Projects)

Start year: 2021

Summary: The project aims to resolve important and longstanding open problems in Geometric Group Theory and Theoretical Computer Science. Since the 1980s researchers have conjectured that the geometric property of being "geodetic" is equivalent to several purely algebraic, algorithmic, and language-theoretic characterisations. The project team's expertise in geodesic properties of groups, the interaction between formal languages and groups, and the theory of rewriting systems, together with recent breakthroughs by the team guarantees that significant results can be expected. Benefits include training research students and postdoctoral researchers in cutting-edge techniques, and advancing knowledge in mathematics and computer science.

Publications:

Elder, M & Piggott, A 2023, 'On groups presented by inverse-closed finite confluent length-reducing rewriting systems', Journal of Algebra, vol. 627, pp. 106-131.
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Elder, M, Piggott, A & Townsend, K 2023, 'On k-geodetic graphs and groups', International Journal of Algebra and Computation, vol. 33, no. 06, pp. 1169-1182.
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Elder, M, Piggott, A & Townsend, K 2023, 'On k-geodetic graphs and groups', International Journal of Algebra and Computation.
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Dietrich, H, Elder, M, Piggott, A, Qiao, Y & Weiß, A 2022, 'The Isomorphism Problem for Plain Groups Is in ΣP3', Leibniz International Proceedings in Informatics, LIPIcs, vol. 219, pp. 26:1-26:14.
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Elder, M & Piggott, A 2022, 'Rewriting systems, plain groups, and geodetic graphs', Theoretical Computer Science, vol. 903, pp. 134-144.
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FOR Codes: Expanding Knowledge, Mathematical Sciences, Information And Computing Sciences, Group theory and generalisations, Coding, information theory and compression