MATHEMATICA BOHEMICA, Vol. 128, No. 2, pp. 179-186 (2003)

Regular, inverse, and completely regular centralizers of permutations

Janusz Konieczny

Janusz Konieczny, Department of Mathematics, Mary Washington College, Fredericksburg, VA 22401, U.S.A., e-mail:

Abstract: 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 $\cs$ to be a regular semigroup, an inverse semigroup, and a completely regular semigroup.

Keywords: semigroup of full transformations, permutation, centralizer, regular, inverse, completely regular

Classification (MSC2000): 20M20

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