Normal subgroups of Abels' groups
\textit{H. Abels} [Lond. Math. Soc. Lect. Note Ser. 36, 205-211 (1979; Zbl 0422.20026)] has shown that for every prime p the group \(T_ p\) of invertible upper triangular matrices of degree 4 over the ring of rationals with denominator a power of p and two (positive) units at the edges of the diagonal is a finitely presented soluble group that does not satisfy the maximal condition for normal subgroups. Here, some further facts about the normal subgroups of \(T_ p\) are obtained. In particular, the maximal normal subgroups of \(T_ p\) are determined and it is shown that \(T_ p\) has countably many normal subgroups, whereas the normal subgroups of the direct square \(T_ p\times T_ p\) have the cardinality of the continuum.
scientific article; zbMATH DE number 3902894