A classification of the abelian minimal closed normal subgroups of locally compact second-countable groups

We classify the locally compact second-countable (l.c.s.c.) groups A that are abelian and topologically characteristically simple. All such groups A occur as the monolith of some soluble l.c.s.c. group G of derived length at most 3; with known exceptions (specifically, when A is Qn or its dual for some nϵN, we can take G to be compactly generated. This amounts to a classification of the possible isomorphism types of abelian chief factors of l.c.s.c. groups, which is of particular interest for the theory of compactly generated locally compact groups.