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On finitely generated Engel branch groups
Jan Moritz Petschick
We construct finitely generated Engel branch groups, answering a question of Fernández-Alcober, Noce and Tracey on the existence of such objects. In particular, the groups construc…
The automorphism group of a multi-GGS group
Jan Moritz Petschick
A multi-GGS-group is a group of automorphisms of a regular rooted tree, generalising the Gupta--Sidki -groups. We compute the automorphism groups of all non-constant multi-GGS-g…
Free polynilpotent groups and the Magnus property
Benjamin Klopsch, Luis Mendonça, Jan Moritz Petschick
Motivated by a classic result for free groups, one says that a group has the Magnus property if the following holds: whenever two elements generate the same normal subgroup of…
Two periodicity conditions for spinal groups
Jan Moritz Petschick
A constant spinal group is a subgroup of the automorphism group of a regular rooted tree, generated by a group of rooted automorphisms and a group of directed automorphisms …