Complex sentence: Using complex coefficients in the construction of the Hopf algebra of rooted trees, the C-valued characters of this complex Hopf algebra form a group, called the complex Butcher group G C.
Split into simpler sentences: Using complex coefficients in the construction of the Hopf algebra of rooted trees one obtains the complex Hopf algebra of rooted trees. Its C-valued characters form a group, called the complex Butcher group G C.