On the CR automorphism group of a certain hypersurface of infinite type in mathbb C²

In this article, we consider $\mathcal{C}^\infty$-smooth real hypersurfaces of infinite type in $\mathbb C^2$. The purpose of this paper is to give explicit descriptions for stability groups of the hypersurface $M(a,\alpha,p,q)$ (see Sec. $1$) and a radially symmetric hypersurface in $\mathbb C^2$.