discrete group
discrete subgroup of a topological group G is a subgroup H such that there is an open cover of H in which every open subset contains exactly one element of H; in other words, the subspace topology of H in G is the discrete topology
arithmetic group
term
lattice
discrete subgroup in a locally compact topological group
space group
symmetry group of a configuration in space
non-Euclidean crystallographic group
discrete group of isometries of the hyperbolic plane. These symmetry groups correspond to the wallpaper groups in euclidean geometry
reflection group
discrete group which is generated by a set of reflections of some space