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Algorithms for computations with Sylow 2-subgroups of symetric groups

Olshevska Vita

Silesian Journal of Pure and Applied Mathematics

2020

vol. 10, iss. 1

103--120

An algorithm to transform n-levels labeled binary rooted trees into elements from Sylow 2-subgroups of symmetric groups of degree 2n is described. The inverse algorithm that on input permutation from a Sylow 2-subgroup of symmetric groups of degree 2n finds a labeled tree is presented. An algorithm for multiplication of labeled trees that correspond to the multiplication of permutations from the Sylow 2-subgroup is introduced. The complexity and correctness of these algorithms are studied.