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arxiv: 1607.03503 · v1 · pith:VNRI7QDQnew · submitted 2016-07-12 · 🧮 math.GR

A Bieberbach theorem for crystallographic group extensions

classification 🧮 math.GR
keywords gammacrystallographicgroupmathrmbieberbachclassesdimensiondimensional
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In this paper we prove that for each dimension $n$ there are only finitely many isomorphism classes of pairs of groups $(\Gamma,\mathrm{N})$ such that $\Gamma$ is an $n$-dimensional crystallographic group and $\mathrm{N}$ is a normal subgroup of $\Gamma$ such that $\Gamma/\mathrm{N}$ is a crystallographic group.

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