1,141 research outputs found
Investigating self-similar groups using their finite -presentation
Self-similar groups provide a rich source of groups with interesting
properties; e.g., infinite torsion groups (Burnside groups) and groups with an
intermediate word growth. Various self-similar groups can be described by a
recursive (possibly infinite) presentation, a so-called finite
-presentation. Finite -presentations allow numerous algorithms for
finitely presented groups to be generalized to this special class of recursive
presentations. We give an overview of the algorithms for finitely -presented
groups. As applications, we demonstrate how their implementation in a computer
algebra system allows us to study explicit examples of self-similar groups
including the Fabrykowski-Gupta groups. Our experiments yield detailed insight
into the structure of these groups
One Relator Quotients of Graph Products
In this paper, we generalise Magnus' Freiheitssatz and solution to the word
problem for one-relator groups by considering one relator quotients of certain
classes of right-angled Artin groups and graph products of locally indicable
polycyclic groups
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