Abstract
A method is obtained for counting the normal subgroups N of a noneuclidean crystallographic groupwithout reflections, with a given finite quotient group ˇ=N; this has applications to the enumeration of regular coverings of orbifolds. The method, which involves Mo« bius inversion and character theory, is also applied to count normal surface subgroups and non-normal sub- groups of finite index in ˇ.
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