Crystallographic groups and their mathematics

DOI10.1216/RMJ-1981-11-4-511zbMath0477.20002MaRDI QIDQ1160741

Daniel R. Farkas

Publication date: 1981

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

surveyGalilean groupEuclidean isometriesnormal subgroup of finite indexalgebraic crystallographic groupscrystallographic groups in n-dimensional spacegeometric crystallographic groupnumber of crystallographic groupstopological crystallogrphic group

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Other geometric groups, including crystallographic groups (20H15) Reflection groups, reflection geometries (51F15) Research exposition (monographs, survey articles) pertaining to group theory (20-02) Orthogonal and unitary groups in metric geometry (51F25)

Related Items

Expanding endomorphisms of crystallographic manifolds, L-groups of crystallographic groups, Self-similar tilings and expanding homomorphisms of groups, Morphisms of crystallographic groups: Kernels and images, A family of irretractable square-free solutions of the Yang-Baxter equation, Learning the model from the data, Anyonic topological order in twisted equivariant differential (TED) K-theory, Equivariant cohomotopy implies orientifold tadpole cancellation, Approximation by group invariant subspaces, The Calabi construction for compact flat orbifolds, Algebraic \(K\)-theory over virtually abelian groups, Extensions of Measures Invariant under Countable Groups of Transformations, Linear groups, Dihedral manifold approximate fibrations over the circle, Homotopy invariance of 4-manifold decompositions: connected sums, Fibered orbifolds and crystallographic groups, On the isometry group of a compact flat orbifold., Retractability of solutions to the Yang–Baxter equation and p-nilpotency of skew braces, The algebra of norms and expanding maps on groups, The structure of group preserving operators, Number of generators of crystallographic groups, Approximation by crystal-refinable functions, Connective Bieberbach groups, Algebraic 𝐾-theory of poly-(finite or cyclic) groups