Remark

With the notations of cor. 2, if one identifies G with $\mathbf{R}^p\times$ $\mathbf{T}^q\times \mathbf{Z}^r\times A$, the subgroup $\mathbf{R}^p\times \mathbf{T}^q$ is the neutral component of G, the subgroup $\mathbf{T}^q\times A$ is its greatest compact subgroup and $\mathbf{T}^q$ is the neutral component of the latter; the integers $p, q, r$ are determined in a unique manner by G according to the preceding remark, and the group A is determined by G up to isomorphism.