Geodesic
Computation of rewriting systems in finite groups
Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 132-134.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: Burnside group, the rewriting system. 
@article{PDMA_2020_13_a38,
     author = {A. A. Kuznetsov},
     title = {Computation of rewriting systems in finite groups},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {132--134},
     publisher = {mathdoc},
     number = {13},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2020_13_a38/}
}
TY  - JOUR
AU  - A. A. Kuznetsov
TI  - Computation of rewriting systems in finite groups
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2020
SP  - 132
EP  - 134
IS  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2020_13_a38/
LA  - ru
ID  - PDMA_2020_13_a38
ER  - 
%0 Journal Article
%A A. A. Kuznetsov
%T Computation of rewriting systems in finite groups
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2020
%P 132-134
%N 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2020_13_a38/
%G ru
%F PDMA_2020_13_a38
A. A. Kuznetsov. Computation of rewriting systems in finite groups. Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 132-134. http://geodesic.mathdoc.fr/item/PDMA_2020_13_a38/

[1] Konstantinova E. V., Kombinatornye zadachi na grafakh Keli, NGU, Novosibirsk, 2010, 110 pp.

[2] Camelo M., Papadimitriou D., Fàbrega L., Vilà P., “Efficient routing in Data Center with underlying Cayley graph”, Proc. 5th Workshop Complex Networks CompleNet, 2014, 189–197

[3] Epstein D., Paterson M., Cannon J., et al., Word Processing in Groups, Jones and Barlett Publ., Boston, 1992, 330 pp. | MR | Zbl

[4] Sims C., Computation with Finitely Presented Groups, Cambridge University Press, Cambridge, 1994, 628 pp. | MR | Zbl

[5] Havas G., Wall G., Wamsley J., “The two generator restricted Burnside group of exponent five”, Bull. Austral. Math. Soc., 1974, no. 10, 459–470 | DOI | MR | Zbl