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Keywords:
semigroup of full transformations; permutation; centralizer; regular; inverse; completely regular semigroups
semigroup of full transformations; permutation; centralizer; regular; inverse; completely regular semigroups
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.
References:
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