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Regular, inverse, and completely regular centralizers of permutations. (English) Zbl 1027.20046
Summary: 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.

##### MSC:
 20M20 Semigroups of transformations, relations, partitions, etc.
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