About the centralizer of an automorphism of order 2 of Burnside group $B_0(2,5)$

The structure of the centralizer of an automorphism of order 2 of a special kind of Burnside group $B_0(2, 5)$ is investigated. The generators, order, nilpotency class and derived length of of the centralizer are computed. The lower and upper central series of of the centralizer are built.