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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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