(algebra, Galois theory) A group which has a chain of subgroups going from itself all the way down to the trivial subgroup, such that any subgroup in the chain is a normal subgroup of the one immediately above it in the chain, and such that the quotient of any subgroup by the normal subgroup immediately under it is a cyclic group.

(mathematics) A group that can be realized geometrically by sequences of reflections across the sides of a triangle.

(group theory) The restricted wreath product mathbf Z₂≀ mathbf Z.

(mathematics) The Chow groups of an algebraic variety over any field are algebro-geometric analogs of the homology of a topological space. The elements of the Chow group are formed out of subvarieties (so-called algebraic cycles) in a similar way to how simplicial or cellular homology groups are formed out of subcomplexes.

(mathematics) Any of seven symmetry groups of infinitely long ornamented bands.

(mathematics) The group of 3×3 upper triangular matrices of the form 1ac\0 1b\0 0 1\ under the operation of matrix multiplication, arising in the description of one-dimensional quantum-mechanical systems.

(algebra) Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;

plural of group chat

A place of residence intended to provide medical care for people with complex health needs.

plural of group home