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Non-Normal Pairs of Non-Euclidean Crystallographic Groups

Authors:	Estevez Jose Luis; Izquierdo Milagros

Institution:	Depto. Matemáticas Fundamentales, Facultad Ciencias, UNED C/Senda del Rey 9, 28040 Madrid, Spain; jestevez{at}mat.uned.es Matematiska Institutionen, Linköpings Universitet 581 83 Linköping, Sweden; miizq{at}mai.liu.se

Abstract:	Let ${Gamma}$ be a non-Euclidean crystallographic group. ${Gamma}$ is said tobe non-maximal if there exists a non-Euclidean crystallographicgroup ${Gamma}$ ' such that ${Gamma}$ $≤$ ${Gamma}$ ' and the dimension of the Teichmüllerspace of ${Gamma}$ equals the dimension of the Teichmüller spaceof ${Gamma}$ '. The full list of such pairs of groups is computed in thecase when ${Gamma}$ is non-normal in ${Gamma}$ '. The corresponding problem forFuchsian groups was solved by Singerman. 2000 Mathematics SubjectClassification 20H10 (primary), 30F10 (secondary).

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