PORTUGALIAE MATHEMATICA Vol. 51, No. 2, pp. 163172 (1994) 

On the Nilpotent Rank of Partial Transformation SemigroupsG.U. GarbaDep. of Mathematical and Computational Sciences, University of St. Andrews,St. Andrews, KY169SS, Fife, Scotland  U.K. Abstract: In [7] Sullivan proved that the semigroup $SP_{n}$ of all strictly partial transformations on the set $X_{n}=\{1,...,n\}$ is nilpotentgenerated if $n$ is even, and that if $n$ is odd the nilpotents in $SP_{n}$ generate $SP_{n}\backslash W_{n1}$ where $W_{n1}$ consists of all elements in $[n1,n1]$ whose completions are odd permutations. We now show that whether $n$ is even or odd both the rank and the nilpotent rank of the subsemigroup of $SP_{n}$ generated by the nilpotents are equal to $n+2$. Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1994 Sociedade Portuguesa de Matemática
