The structure of 0-bisimple strongly \(E^*\)-unitary inverse monoids.
Let \(G\) be a group and let \(P\) be a submonoid of \(G\). For each \(x\in G\), let \(\beta_x\) be the partial permutation of \(P\) given by \(\beta_x(t)=xt\). Let \(S_1(G,P)\) be the inverse submonoid of \(I(P)\) generated by the \(\beta_x\) with \(x\in G\) and let \(S_2(G,P)\) be the inverse submonoid of \(I(P)\) generated by the \(\beta_x\) with \(x\in P\). The main results in the paper may be summarized as follows: a characterization of 0-bisimple strongly \(E^*\)-unitary inverse monoids as monoids of the form \(S_2(G,P)\); and a characterization of 0-bisimple strongly \(F^*\)-unitary inverse monoids as monoids of the form \(S_1(G,P)\).
scientific article; zbMATH DE number 1972511