Non-Normal Pairs of Non-Euclidean Crystallographic Groups

Let Γ be a non-Euclidean crystallographic group. Γ is said to be non-maximal if there exists a non-Euclidean crystallographic group Γ′ such that Γ ⩽ Γ′ and the dimension of the Teichmüller space of Γ equals the dimension of the Teichmüller space of Γ′. The full list of such pairs of groups is computed in the case when Γ is non-normal in Γ′. The corresponding problem for Fuchsian groups was solved by Singerman. 2000 Mathematics Subject Classification 20H10 (primary), 30F10 (secondary).