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The point group C_1 is a group on a single element that is isomorphic to the trivial group. Its character table is given below. C_1 1 1 1

Two lines or plane congruent geometric figures which lie on top of each other are said to be coincident.

Given a set S of points in the plane, an enclosing circle is a circle for which all points S lie in its interior.

The Killing form is an inner product on a finite dimensional Lie algebra g defined by B(X,Y)=Tr(ad(X)ad(Y)) (1) in the adjoint representation, where ad(X) is the adjoint ...

The image of A_5×A_5 in the special orthogonal group SO(4), where A_5 is the icosahedral group.

The homeomorphism group of a topological space X is the set of all homeomorphisms f:X->X, which forms a group by composition.

The structure constant is defined as iepsilon_(ijk), where epsilon_(ijk) is the permutation symbol. The structure constant forms the starting point for the development of Lie ...

One of the symmetry groups of the Platonic solids. There are three polyhedral groups: the tetrahedral group of order 12, the octahedral group of order 24, and the icosahedral ...

A permutation group in which the permutations are limited to transpositions.

The free part of the homology group with a domain of coefficients in the group of integers (if this homology group is finitely generated).