Geodesic
Green’s relations and regularity in centralizers of permutations
Glasgow mathematical journal, Tome 41 (1999) no. 1, pp. 45-57

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For any permutation σ on N = {1,2,...,n}: (i) Green’s relations are characterized in the centralizer C(σ) of σ (relative to the semigroup PTn of partial transformations on N); and (ii) a criterion is given for C(σ) to be a regular semigroup (inverse semigroup, union of groups). 
KONIECZNY, JANUSZ. Green’s relations and regularity in centralizers of permutations. Glasgow mathematical journal, Tome 41 (1999) no. 1, pp. 45-57. doi: 10.1017/S0017089599970301
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