group homomorphism

The group homomorphism is given in the following way.

Then the functions may be added pointwise to produce a group homomorphism.

The fact that this function is a surjective group homomorphism follows directly.

In general, the trace is not a group homomorphism, nor does the set of traces form a group.

Then a group homomorphism is continuous if and only if it has open kernel.

A group homomorphism is a homomorphism between two groups.

Then and hence is a group homomorphism.

Note that f is indeed a group homomorphism from G to H:

This gives us an Abelian hidden subgroup problem, as f corresponds to a group homomorphism.

Let be a Lie group homomorphism and let be its derivative at the identity.

The first is that it is not obvious that this yields a group homomorphism, or even a map at all.

The purpose of defining a group homomorphism as it is, is to create functions that preserve the algebraic structure.

Then the map from the group of points on to the Jacobian of defined by is a group homomorphism.

Let be a non-zero complex-analytic group homomorphism.

Boundary monomorphisms for all edges e of A, so that each α is an injective group homomorphism.

The commutativity of H is needed to prove that h + k is again a group homomorphism.

A group homomorphism between dimension group is said to be contractive if it is scale-preserving.

Since a group homomorphism preserves identity elements, the identity element e of G must belong to the kernel.

The modular function is a continuous group homomorphism into the multiplicative group of nonzero real numbers.

There is a natural group homomorphism PH H which sends each path to its endpoint.

The notions of group homomorphism, subgroup, normal subgroup and the isomorphism theorems are typical examples.

For two left -modules , a group homomorphism is called homomorphism of -modules if .

For the smallest positive integer such that there exists a computable injective group homomorphism from the subgroup of of order to .

A group homomorphism f: G H can then be considered as a functor, which makes G into a H-category.

Many concepts of group theory generalize to groupoids, with the notion of functor replacing that of group homomorphism.