1 citations · 2 across the 10 of their papers we have counts for
13 papers
Only their cardinality can prevent groups from being quotients of weakly branch groups
J. Moritz Petschick
It is a well-known fact that every proper quotient of a branch group is a virtually abelian group. We record that every group of cardinality at most is a quotient of…
Representation zeta functions of split extensions of
J. Moritz Petschick, Margherita Piccolo
We consider the representation growth of split extensions of . We prove that the corresponding representation zeta functions factor as a product of the representation ze…
Branch groups with many maximal subgroups
J. Moritz Petschick
This article presents the construction of finitely generated branch groups with uncountably many maximal subgroups using embedding techniques. This addresses a question posed by Gr…
Conciseness of first-order formulae
Martina Conte, Jan Moritz Petschick
A word is concise in a class of groups if, for every group in , the verbal subgroup is finite whenever takes only finitely many values…
Maximal subgroups in torsion branch groups
Mikel Eguzki Garciarena, J. Moritz Petschick
We study the maximal subgroups of branch groups and obtain a criterion that ensures that certain spinal groups are contained in the class of groups with all maximal…
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…
The derived series of GGS-groups
Jan Moritz Petschick
Given a GGS-group with non-constant defining tuple over a prime-regular rooted tree, we calculate the indices and describe the structure of the higher derived sub…
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…
Conjugacy classes of polyspinal groups
Jan Moritz Petschick, Anitha Thillaisundaram
Spinal groups and multi-GGS groups are both generalisations of the well-known Grigorchuk-Gupta-Sidki (GGS-)groups. Here we give a necessary condition for spinal groups to be conjug…
Groups of small period growth
Jan Moritz Petschick
We construct finitely generated groups of small period growth, i.e. groups where the maximum order of an element of word length grows very slowly in . This answers a questio…
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 …
On the Basilica Operation
Jan Moritz Petschick, Karthika Rajeev
Inspired by the Basilica group , we describe a general construction which allows us to associate to any group of automorphisms of a roote…