M. E. Garciarena

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math.GR2026

Spinal Hanoi Towers Groups

Francesca Cavalieri, Mikel E. Garciarena, Marialaura Noce

We introduce and study \emph{spinal Hanoi towers groups}, a family of groups acting on the $d$ -adic tree that contains both the classical Hanoi towers group $H^{(3)}$ and…

math.GR2024

On the lower central series of a large family of non-periodic GGS-groups

Gustavo A. FernÃ¡ndez-Alcober, Mikel E. Garciarena, Marialaura Noce

For an odd prime $p$ , we determine the lower central series of a large family of non-periodic GGS-groups, which has a density of roughly $(\frac{p - 1}{p})^{2}$ within all GGS-groups.…

math.GR2024

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 $M F$ of groups with all maximal…