Some subgroups of the burnside group | Applied Discrete Mathematics. Supplement. 2021. № 14. DOI: 10.17223/2226308X/14/43

Some subgroups of the burnside group

B_o(2,5). Let B_o(2,5) = (x,y> be the largest finite two generator Burnside group of exponent five and order 5³⁴. We study a series of subgroups H_i = (a_i,b_i> of the group B_o(2, 5), where a₀ = x, b₀ = y, a_i = a_i-1b_i_₁ and b_i = b_i-1 a_i-1 for i G N. It has been found that H4 is a commutative group. Therefore, H5 is a cyclyc group and the series of subgroups is broken. The elements a₄ = xy²xyx²y²x²yxy²x and b₄ = yx²yxy²x²y²xyx²y of length 16 generate an abelian subgroup of order 25 in Bo(2, 5). Using computer calculations, we have found that there is no other pair of group words of length less than 16 that generate a noncyclic abelian subgroup in Bo(2, 5).

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Keywords

non-commutative cryptography, Burnside group

Authors

Name	Organization	E-mail
Kuznetsov A. A.	Siberian State University of Science and Technology named after Academician M.F. Reshetnev	alex_kuznetsov80@mail.ru
Kuznetsova A. S.	Krasnoyarsk State Agrarian University	alexakuznetsova85@gmail.com

Всего: 2

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