Abstract
ABSTRACT In this short note, we show that the number of monogenic submonoids of the full transformation monoid of degree n for , equals the sum of the number of cyclic subgroups of the symmetric groups on 1 to n points. We also prove an analogous statement for monogenic subsemigroups of the finite full transformation monoids, as well as monogenic inverse submonoids and subsemigroups of the finite symmetric inverse monoids.
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