In the paper 'FINITE LINEAR GROUPS WHOSE RING OF INVARIANTS IS A COMPLETE INTERSECTION' by VICTOR KAC AND KEI-ICHI WATANABE published in BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 6, Number 2, March 1982, it is said in remark 2 of page no 222 that for any finite subgroup $G$ of $GL_2(\mathbb{C})$ the ring of invariance $\mathbb{C}[X_1, X_2]^G$ is always a complete itersection ring without any reference. Can anyone kindly tell me a reference for this result? Thanking you.