The rank of the endomorphism monoid of a uniform partition. (English) Zbl 1176.20059
The authors prove that the minimal possible cardinality for a generating set of the semigroup of all transformations of a finite set of cardinality at least three that leave a nontrivial uniform partition invariant equals four. For two other semigroups of all transformations which preserve (in a certain sense) the equivalence relation determined by a uniform partition as above it is shown that the minimal possible cardinality for a generating set is three.
Reviewer: Volodymyr Mazorchuk (Uppsala)
MSC:
| 20M20 | Semigroups of transformations, relations, partitions, etc. |
| 20M05 | Free semigroups, generators and relations, word problems |
Keywords:
transformation semigroups; generating sets; endomorphism monoids; uniform partitions; wreath products; relative ranksReferences:
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