(group theory) Any one of the 26 exceptional finite simple groups, which do not belong to any of the general, infinite categories specified by the classification theorem for finite simple groups.

(group theory) A group obtained from a larger group by aggregating elements via an equivalence relation that preserves group structure.

(group theory) The unique group (up to isomorphism) consisting of a single element (which is the identity element).

(group theory) A group which has no normal subgroups apart from the trivial group and itself.

(group theory) A group generated by a single element.

(algebra) The group of all complex numbers of unit modulus, with the group operation being complex multiplication.

(mathematics) For a field K, an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras.

(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.