Computation of rewriting systems in finite groups | Applied Discrete Mathematics. Supplement. 2020. № 13. DOI: 10.17223/2226308X/13/39

Computation of rewriting systems in finite groups

We present an algorithm computing the rewriting system R of a finite group generated by the fixed set of elements. We have proved that R is confluent and irreducible in this case. A necessary condition for the effective implementation of the algorithm is the availability of a fast procedure for multiplying elements in the group. For example, this group operation can be a composition of permutations, matrix multiplication, calculation of Hall's polynomials, etc. We study rewriting systems in finite two-generator groups of exponent five using the algorithm.

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Keywords

система переписывающих правил, группа Бернсайда, Burnside group, the rewriting system

Authors

Name	Organization	E-mail
Kuznetsov A. A.	Siberian State University of Science and Technology named after academician M.F. Reshetneva	alex_kuznetsov80@mail.ru

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References

Константинова Е. В. Комбинаторные задачи на графах Кэли. Новосибирск: НГУ, 2010. 110с.

Camelo M., Papadimitriou D., Fabrega L., and Vila P. Efficient routing in Data Center with underlying Cayley graph // Proc. 5th Workshop Complex Networks CompleNet. 2014. P. 189197.

Epstein D., Paterson M., Cannon J., et al. Word Processing in Groups. Boston: Jones and Barlett Publ., 1992. 330 p.

Sims C. Computation with Finitely Presented Groups. Cambridge: Cambridge University Press, 1994. 628 p.

Havas G., Wall G., and Wamsley J. The two generator restricted Burnside group of exponent five // Bull. Austral. Math. Soc. 1974. No. 10. P. 459-470.