Search Results for ""

Given a knot diagram, it is possible to construct a collection of variables and equations, and given such a collection, a group naturally arises that is known as the group of ...

An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the ...

The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, ...

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 which is related to the Taniyama-Shimura conjecture.

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 solvable Lie group is a Lie group G which is connected and whose Lie algebra g is a solvable Lie algebra. That is, the Lie algebra commutator series ...

A group G is said to act on a set X when there is a map phi:G×X->X such that the following conditions hold for all elements x in X. 1. phi(e,x)=x where e is the identity ...

The group D_5 is one of the two groups of order 10. Unlike the cyclic group C_(10), D_5 is non-Abelian. The molecule ruthenocene (C_5H_5)_2Ru belongs to the group D_(5h), ...

The group direct sum of a sequence {G_n}_(n=0)^infty of groups G_n is the set of all sequences {g_n}_(n=0)^infty, where each g_n is an element of G_n, and g_n is equal to the ...