The structure of Cartan subgroups in Lie groups

We study properties and the structure of Cartan subgroups in a connected Lie group. obtain characterisation which generalises W\"ustner's theorem for same. show that are same as those centralizers maximal compact radical. Moreover, we describe recipe constructing containing certain nilpotent solvable characterise quotient group modulo closed normal subgroup images ambient also density power maps on image any $k$-th map has dense if its restriction to corresponding have images.