So I'm looking to find the maximal abelian subgroup of SL(3,C). I know that if a maximal torus for SL(3,C) exists that said torus is the maximal abelian subgroup. Is it enough to know that since SU(3) is a subgroup that they have the same maximally abelian subgroup (namely, a maximal torus of SU(3))? Is there a simple way to go about showing that they share this maximal abelian subgroup?
Apologies if the wording lacks precision, feel free to guide me toward clarifications.