Geodesic
Regular, inverse, and completely regular centralizers of permutations
Mathematica Bohemica, Tome 128 (2003) no. 2, pp. 179-186.

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For an arbitrary permutation $\sigma $ in the semigroup $T_n$ of full transformations on a set with $n$ elements, the regular elements of the centralizer $C(\sigma )$ of $\sigma $ in $T_n$ are characterized and criteria are given for $C(\sigma )$ to be a regular semigroup, an inverse semigroup, and a completely regular semigroup.
DOI : 10.21136/MB.2003.134038
Classification : 20M17, 20M18, 20M20
Keywords: semigroup of full transformations; permutation; centralizer; regular; inverse; completely regular semigroups 
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Konieczny, Janusz. Regular, inverse, and completely regular centralizers of permutations. Mathematica Bohemica, Tome 128 (2003) no. 2, pp. 179-186. doi : 10.21136/MB.2003.134038. http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134038/

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