An extending method in transformation semigroups (Q2779054)

Let \(\Omega\) be a set with \(X\) a subset of \(\Omega\). Let \(G\) be a subgroup of the full symmetric group \(S_X\) and let \(e\) be an idempotent in the full transformation semigroup \(T_\Omega\) whose range is \(X\). The main construction of the paper is that of an orthodox subsemigroup \(G(e)\) of \(T_\Omega\) that contains \(e\) and is such that the set of restrictions of the members of \(G(e)\) to \(X\) forms a group isomorphic to the given group \(G\).