Geodesic
Isolated and nilpotent subsemigroups in the variants of $\mathcal{IS}_n$
Algebra and discrete mathematics, no. 1 (2006), pp. 89-97.

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All isolated, completely isolated, and nilpotent subsemigroups in the semigroup $\mathcal{IS}_n$ of all injective partial transformations of an $n$-element set, considered as a semigroup with a sandwich multiplication are described.
Keywords: Inverse symmetric semigroup, variants of a semigroup, sandwich semigroup, isolated subsemigroups, nilpotent subsemigroups. 
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     author = {Galyna Tsyaputa},
     title = {Isolated and nilpotent subsemigroups in the variants of $\mathcal{IS}_n$},
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     url = {http://geodesic.mathdoc.fr/item/ADM_2006_1_a7/}
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Galyna Tsyaputa. Isolated and nilpotent subsemigroups in the variants of $\mathcal{IS}_n$. Algebra and discrete mathematics, no. 1 (2006), pp. 89-97. http://geodesic.mathdoc.fr/item/ADM_2006_1_a7/