Transitive powers of Young-Jucys-Murphy elements are central

I. P. Goulden, D. M. Jackson

Although powers of the Young-Jucys-Murphya elements X_i = (1 i) + ... +(i-1 i), i = 1, ..., n, in the symmetric group S_n acting on {1, ...,n} do not lie in the centre of the group…