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Free semigroups in wreath powers of transformation semigroups. (English) Zbl 1212.20074

Summary: It is established a criterion when the infinite wreath power of a finite transformation semigroup contains a free subsemigroup. It is shown that the infinite wreath power of a transformation semigroup either contains no free non-commutative subsemigroups or most of its finitely generated subsemigroups are free.

MSC:

20M05 Free semigroups, generators and relations, word problems
20M20 Semigroups of transformations, relations, partitions, etc.
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