The isomorphism problem for orthodox semigroups (Q1821875)

The author's structure theorem for orthodox semigroups [ibid. 39, 677-686 (1971; Zbl 0232.20124)] produced an orthodox semigroup \({\mathcal H}(E,T,\psi)\) from a band \(E\), an inverse semigroup \(T\) and a morphism \(\psi\) between two inverse semigroups, namely \(T\) and \(W_ E/\gamma\), an inverse semigroup constructed from \(E\). Here, we solve the isomorphism problem: when are two such orthodox semigroups isomorphic? This leads to a way of producing all orthodox semigroups, up to isomorphism, with prescribed band \(E\) and maximum inverse semigroup morphic image \(T\).