An algorithm for computation of the growth functions in finite two-generated groups of exponent 5 | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2016. № 3(33). DOI: 10.17223/20710410/33/10

Let B₀(2, 5) = (a₁,a₂) be the largest 2-generator Burnside group of exponent 5. It has the order 5. There is a power commutator representation of B₀(2, 5). In this case, every element of the group can be uniquely represented as aQ • aQ • ... • aQ|, where a_i e Z₅, a_i e B₀(2, 5), i = 1, 2,..., 34. Here, a₁ and a₂ are generators of B₀(2, 5), commutators a₃,...,a₃₄ are recursively defined by a₁ and a₂. We define B_k = B₀(2, 5)/(a_k+1,..., a₃₄) as a quotient of B₀(2, 5). It is clearly that |B_k| = 5. A new algorithm for computing the growth function of Bk is created. Using this algorithm, we calculated the growth functions of B_k relative to generating sets {a₁, a₂} and {a₁, a-, a₂, a-} for k = 15, 16, 17.