Discrete groups

symmetry group of a configuration in space

subgroup of a real vector space

mathematical classification of a two-dimensional repetitive pattern

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

classification system for crystals

type of symmetry group

discrete subgroup of the real projective special linear group of dimension 2

theorem about sufficient conditions for ensuring that that several elements in a group acting on a set freely generate a free subgroup of that group

discrete group of Möbius transformations