Definition
Given two groups, {% G %} and {% H %}, a homomorphism is a function from {% G %} to {% H %} such that
{% f(hg) = f(h)f(g) %}
for {% h %} and {% g %} in {% G %}.
Definitions
- Isomorphism - a homomorphism that is both injective and surjective.
- Kernel - the kernel of a homomorphism is the set in the domain that maps to the identity element in the range.
Theorems
For a homomorphism {% f : G \rightarrow H %}
- {% f(e) = e %}
- {% f(g^{-1}) = f(g)^{-1} %}