Search Results for ""

The cyclic group C_9 is one of the two Abelian groups of group order 9 (the other order-9 Abelian group being C_3×C_3; there are no non-Abelian groups of order 9). An example ...

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 ...

A group of linear fractional transformations which transform the arguments of Kummer solutions to the hypergeometric differential equation into each other. Define A(z) = 1-z ...

The general orthogonal group GO_n(q,F) is the subgroup of all elements of the projective general linear group that fix the particular nonsingular quadratic form F. The ...

A particular type of automorphism group which exists only for groups. For a group G, the inner automorphism group is defined by Inn(G)={sigma_a:a in G} subset Aut(G) where ...

A finitely generated discontinuous group of linear fractional transformations z->(az+b)/(cz+d) acting on a domain in the complex plane. The Apollonian gasket corresponds to a ...

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, ...

The first group isomorphism theorem, also known as the fundamental homomorphism theorem, states that if phi:G->H is a group homomorphism, then Ker(phi)⊴G and ...

C_5 is the unique group of group order 5, which is Abelian. Examples include the point group C_5 and the integers mod 5 under addition (Z_5). No modulo multiplication group ...