Algebra Seminar talk

Elisabeth Fink
Automorphism Groups of Non-Regular Rooted Trees

I will describe a certain class of finitely generated but not finitely presented auto- morphism groups on non-regular rooted trees. These groups will be shown to be a branch group which is not just-infinite. Using rather basic properties I will derive a few facts about the group structure. In particular I am going to outline why in such groups every normal subgroup is finitely generated (the groups have max-n). Mentioning a rather technical result about abelianisations of subgroups I will show that the group is not just-infinite. Using this I will further prove that it has infinite virtual first betti number. I will then explain why these groups are not large.