Recent work in the theory of locally compact second-countable (l.c.s.c.) groups has highlighted the importance of chief factors, meaning pairs of closed normal subgroups K/L such that no closed normal subgroups lie strictly between K and L. In particular, the group K/L is then topologically characteristically simple, meaning it has no proper nontrivial closed subgroup that is preserved by all automorphisms. I will present a classification of the abelian l.c.s.c. topologically characteristically simple groups: these all occur as chief factors of soluble groups, and naturally fall into five families with a few parameters. Each family has a straightforward characterization within the class of abelian l.c.s.c. groups, without directly invoking the property of being topologically characteristically simple.
This video was uploaded to YouTube by Newcastle University, Australia. It is part of the 64th annual meeting of the Australian Mathematical Society, which was held (virtually) at the University of New England.
