Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Petschick, Jan Moritz"'
Autor:
Petschick, Jan Moritz
We construct finitely generated Engel branch groups, answering a question of Fern\'andez-Alcober, Noce and Tracey on the existence of such objects. In particular, the groups constructed are not nilpotent, yielding the second known class of examples o
Externí odkaz:
http://arxiv.org/abs/2308.01968
Autor:
Petschick, Jan Moritz
A multi-GGS-group is a group of automorphisms of a regular rooted tree, generalising the Gupta--Sidki $p$-groups. We compute the automorphism groups of all non-constant multi-GGS-groups.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/2209.00899
Autor:
Petschick, Jan Moritz
Given a GGS-group $G$ with non-constant defining tuple over a prime-regular rooted tree, we calculate the indices $|G:G^{(n)}|$ and describe the structure of the higher derived subgroups $G^{(n)}$ for all $n \in \mathbb{N}$. We find that the values $
Externí odkaz:
http://arxiv.org/abs/2208.14975
Motivated by a classic result for free groups, one says that a group $G$ has the Magnus property if the following holds: whenever two elements generate the same normal subgroup of $G$, they are conjugate or inverse-conjugate in $G$. It is a natural p
Externí odkaz:
http://arxiv.org/abs/2208.13691
Autor:
Petschick, Jan Moritz
We construct finitely generated groups of small period growth, i.e. groups where the maximum order of an element of word length $n$ grows very slowly in $n$. This answers a question of Bradford related to the lawlessness growth of groups and is conne
Externí odkaz:
http://arxiv.org/abs/2201.04525
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 conjugate, and we establish a necessary and sufficient condition for multi-G
Externí odkaz:
http://arxiv.org/abs/2201.03266
Autor:
Petschick, Jan Moritz
A constant spinal group is a subgroup of the automorphism group of a regular rooted tree, generated by a group of rooted automorphisms $A$ and a group of directed automorphisms $B$ whose action on a subtree is equal to the global action. We provide t
Externí odkaz:
http://arxiv.org/abs/2112.12428
Inspired by the Basilica group $\mathcal B$, we describe a general construction which allows us to associate to any group of automorphisms $G \leq \operatorname{Aut}(T)$ of a rooted tree $T$ a family of Basilica groups $\operatorname{Bas}_s(G), s \in
Externí odkaz:
http://arxiv.org/abs/2103.05452
Autor:
Petschick, Jan Moritz
Publikováno v:
Journal of Algebra & Its Applications; Dec2024, Vol. 23 Issue 14, p1-24, 24p
