Iwasawa's Local Splitting Theorem for Pro-Lie Groups

Abstract

If the nilradical 𝔫(𝔤) of the Lie algebra 𝔤 of a pro-Lie group G is finite dimensional modulo the center 𝔷(𝔤), then every identity neighborhood U of G contains a closed normal subgroup N such that G/N is a Lie group and G and N × G/N are locally isomorphic.