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

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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/}
}
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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/