Magnus pairs in, and free conjugacy separability of, limit groups
Larsen Louder, Nicholas W.M. Touikan
TL;DR
This paper investigates the properties of limit groups, focusing on Magnus pairs and free conjugacy separability, revealing that some limit groups have non-conjugate elements that become conjugate in all free quotients, while towers over free groups are freely conjugacy separable.
Contribution
It demonstrates the existence of Magnus pairs in certain limit groups and establishes the free conjugacy separability of towers over free groups, advancing understanding of their algebraic structure.
Findings
Limit groups can have non-conjugate elements whose images are conjugate in all free quotients.
Towers over free groups are proven to be freely conjugacy separable.
The results clarify the conjugacy properties within limit groups and their quotients.
Abstract
There are limit groups having non-conjugate elements whose images are conjugate in every free quotient. Towers over free groups are freely conjugacy separable.
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