Free pro nite semigroups over semidirect products
نویسنده
چکیده
We give a general description of the free proonite semigroups over a semidirect product of pseudovarieties. More precisely, A (V W) is described as a closed subsemigroup of a proonite semidirect product of the form A WA V A W. As a particular case, the free proonite semigroup over J 1 V is described in terms of the geometry of the Cayley graph of the free proonite semigroup over V (here J 1 is the pseudovariety of semilattice monoids). Applications are given to the calculations of the free proonite semigroup over J 1 Nil and of the free proonite monoid over J 1 G (where Nil is the pseudovariety of nite nilpotent semigroups and G is the pseudovariety of nite groups). The latter free proonite monoid is compared with the free proonite inverse monoid, which is also calculated here.
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