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Preprint Number 1664
1664. Montserrat Casals-Ruiz, Albert Garreta, Javier de la Nuez González On the positive theory of groups acting on trees E-mail: Submission date: 20 October 2019 Abstract: We study the positive theory of groups acting on trees and show that under
the presence of weak small cancellation elements, the positive theory of the
group is trivial, i.e. coincides with the positive theory of a
non-abelian free
group. Our results apply to a wide class of groups, including non-virtually
solvable fundamental groups of 3-manifold groups, generalised
Baumslag-Solitar groups and almost all one-relator groups and graph
products of
groups. It follows that groups in the class satisfy a number of algebraic
properties: for instance, their verbal subgroups have infinite width and,
although some groups in the class are simple, they cannot be boundedly
simple. Mathematics Subject Classification: 20E08, 20E06, 20F06, 20F70, 03C07 Keywords and phrases: |
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