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arxiv: 1501.03648 · v1 · pith:NNEX43XWnew · submitted 2015-01-15 · 🧮 math.GR

Crystallographic groups with trivial center and outer automorphism group

classification 🧮 math.GR
keywords groupcrystallographictrivialautomorphismcentermathbboutercocompact
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Let $\Gamma$ be a crystallographic group of dimension $n,$ i.e. a discrete, cocompact subgroup of $\operatorname{Isom}(\mathbb{R}^n)$ = $O(n)\ltimes\mathbb{R}^n.$ For any $n\geq 2,$ we construct a crystallographic group with a trivial center and a trivial outer automorphism group.

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