Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/16882

 Title: Inverse semigroups generated by nilpotent transformations Author(s): Howie, John M.Smith, M. Paula Marques Keywords: Inverse semigroupNilpotentsTransformationsCongruences Issue date: 1984 Publisher: Cambridge University Press Journal: Proceedings of the Royal Society of Edinburgh Abstract(s): Let $X$ be a set with infinite cardinality $m$ and let $B$ be the Baer-Levi semigroup, consisting of all one-one mappings $a:X\rightarrow X$ for which $∣X\Xα∣ = m$. Let $K_m=$, the inverse subsemigroup of the symmetric inverse semigroup $\mathcal T(X)$ generated by all products $\beta^{−1}\gamma$, with $\beta,1\gamma\in B$. Then $K_m =$, where $N_2$ is the subset of $\mathcal T(X)$ consisting of all nilpotent elements of index 2. Moreover, $K_m$ has 2-nilpotent-depth 3, in the sense that $N_2\cup N_2^2\subset K_m = N_2\cup N_2^2\cup N_2^3$. Let $P_m$ be the ideal \$\{\alpha\in K_m: ∣dom \alpha∣

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