Commensurators of thin normal subgroups and abelian quotients (Q6596251)

The paper is devoted to a problem of characterizing the discreteness of subgroups within a subgroup of a rank-one Lie group. The authors show that the commensurator of an infinite normal subgroup \(K\) of a discrete subgroup \(\Gamma\) in a rank-one Lie group \(G\) is discrete if and only if the infinite quotient \(Q = \Gamma/K\) admits a surjective homomorphism onto the group of integers \(\mathbb Z\) and that the commensurator \(\mathrm{Comm}_G(K)\) contains the normalizer \(\mathrm{Norm}_G(K)\) with finite index (Theorems 1.3, 5.1).