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C_6 is one of the two groups of group order 6 which, unlike D_3, is Abelian. It is also a cyclic. It is isomorphic to C_2×C_3. Examples include the point groups C_6 and S_6, ...

Two representations of a group chi_i and chi_j are said to be orthogonal if sum_(R)chi_i(R)chi_j(R)=0 for i!=j, where the sum is over all elements R of the representation.

Let L be a finite-dimensional split semisimple Lie algebra over a field of field characteristic 0, H a splitting Cartan subalgebra, and Lambda a weight of H in a ...

The dihedral group D_6 gives the group of symmetries of a regular hexagon. The group generators are given by a counterclockwise rotation through pi/3 radians and reflection ...

If two groups are residual to a third, every group residual to one is residual to the other. The Gambier extension of this theorem states that if two groups are ...

The dihedral group D_4 is one of the two non-Abelian groups of the five groups total of group order 8. It is sometimes called the octic group. An example of D_4 is the ...

Given a triangle with angles (pi/p, pi/q, pi/r), the resulting symmetry group is called a (p,q,r) triangle group (also known as a spherical tessellation). In three ...

A group representation of a group G on a vector space V can be restricted to a subgroup H. For example, the symmetric group on three letters has a representation phi on R^2 ...

The projective special unitary group PSU_n(q) is the group obtained from the special unitary group SU_n(q) on factoring by the scalar matrices contained in that group. ...

Given two groups G and H, there are several ways to form a new group. The simplest is the direct product, denoted G×H. As a set, the group direct product is the Cartesian ...