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.
View/Download from: Publisher's site

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.
View/Download from: Publisher's site

Elder, M, Piggott, A & Townsend, K 2023, 'On k-geodetic graphs and groups', International Journal of Algebra and Computation.
View/Download from: Publisher's site

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.
View/Download from: Publisher's site

Elder, M & Piggott, A 2022, 'Rewriting systems, plain groups, and geodetic graphs', Theoretical Computer Science, vol. 903, pp. 134-144.
View/Download from: Publisher's site

Elder, M, Piggott, A, Stober, F, Thumm, A & Weiß, A, 'Finite Groups with Geodetic Cayley Graphs', Experimental Mathematics, pp. 1-24.
View/Download from: Publisher's site

FOR Codes: Expanding Knowledge, Mathematical Sciences, Information And Computing Sciences, Group theory and generalisations, Coding, information theory and compression

Acknowledgement of Country

UTS acknowledges the Gadigal people of the Eora Nation, the Boorooberongal people of the Dharug Nation, the Bidiagal people and the Gamaygal people, upon whose ancestral lands our university stands. We would also like to pay respect to the Elders both past and present, acknowledging them as the traditional custodians of knowledge for these lands.