The Main Decomposition of Finite-Dimensional Protori
A protorus is a compact connected abelian group of finite dimension. We use a result on finite-rank torsion-free abelian groups and Pontryagin duality to considerably generalize a well-known factorization of a finite-dimensional protorus into a product of a torus and a torus free complementary factor. We also classify direct products of protori of dimension 1 by means of canonical “type” subgroups. In addition, we produce the duals of some fundamental theorems of discrete abelian groups.
Lewis, W., Loth, P., & Mader, A. (2021). The main decomposition of finite-dimensional protori, Journal of Group Theory, 24(1), 109-127. Doi: 10.1515/jgth-2020-0079