In the case of a trivial extension B=C⋉E, we give necessary and sufficient conditions for each e506af14f07d1da69bfed88cf" title="Click to view the MathML source">φn to be surjective. We prove the surjectivity of φ1 for a class of trivial extensions that includes relation extensions and hence cluster-tilted algebras. Finally, we study the kernel of φ1 for any trivial extension, and give a more precise description of this kernel in the case of relation extensions.