6 papers
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 -adic tree that contains both the classical Hanoi towers group and…
On the lower central series of a large family of non-periodic GGS-groups
Gustavo A. Fernández-Alcober, Mikel E. Garciarena, Marialaura Noce
For an odd prime , we determine the lower central series of a large family of non-periodic GGS-groups, which has a density of roughly within all GGS-groups.…
On verbal subgroups of the group of automorphisms of regular rooted trees
Costantino Delizia, Mikel E. Garciarena, Marialaura Noce
In this paper we revisit the description of all verbal subgroups of the group of automorphisms of a regular rooted tree , for and odd.
Applications of Automaton Groups in Cryptography
Delaram Kahrobaei, Marialaura Noce, Emanuele Rodaro
In 1991 the first public key protocol involving automaton groups has been proposed. In this paper we give a survey about algorithmic problems around automaton groups which may have…
Powerful 3-Engel groups
Iker de las Heras, Marialaura Noce, Gunnar Traustason
In this paper we study powerful 3-Engel groups. In particular, we find sharp upper bounds for the nilpotency class of powerful 3-Engel groups and the subclass of powerful metabelia…
On the structure of finite groups determined by the arithmetic and geometric means of element orders
Valentina Grazian, Carmine Monetta, Marialaura Noce
In this paper we consider two functions related to the arithmetic and geometric means of element orders of a finite group, showing that certain lower bounds on such functions stron…