The Largest Subsemilattices of the Semigroup of Transformations on a Finite Set

Details The Largest Subsemilattices of the Semigroup of Transformations on a Finite Set The Largest Subsemilattices of the Semigroup of Transformations on a Finite Set

2010-07-27

arxiv.org/abs/1007.4845v1

Mathematics

Group Theory

7 pages

Scientific paper

Let T(X) be the semigroup of full transformations on a finite set X with n
elements. We prove that every subsemilattice of T(X) has at most 2^{n-1}
elements and that there are precisely n subsemilattices of size exactly
2^{n-1}, each isomorphic to the semilattice of idempotents of the symmetric
inverse semigroup on a set with n-1 elements.

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