Combinatorially factorizable inverse monoids (Q1300597)

An inverse semigroup \(S\) is combinatorially factorizable if there exist a combinatorial inverse subsemigroup \(T\) of \(S\) and a group \(G\) such that \(S=TG\). Combinatorially factorizable semigroups which are cryptic are investigated. Such semigroups are shown to be precisely the idempotent-separating extensions (of a certain kind) of factorizable Clifford semigroups by combinatorially inverse semigroups. Moreover, all combinatorially factorizable submonoids of a cryptic inverse monoid are constructed.