The Boone--Higman Conjecture for groups acting on locally finite trees

  • Venue:

    Geb. 20.30, SR 2.058

  • Date:

    28.11.2024

  • Speaker:

    Claudio Llosa Isenrich

  • Time:

    15:45 Uhr

  • Abstract: The Boone--Higman Conjecture asserts that a finitely generated group has solvable word problem if and only if it embeds in a finitely presented simple group. While it has recently been confirmed for many interesting classes of groups, including hyperbolic groups and virtually special groups, it remains wide open in general. In this talk we explain a method for proving the Boone--Higman Conjecture for groups acting on locally finite trees, which may offer a route for proving it for many new classes of groups. We illustrate our method by showing the Boone--Higman Conjecture for all (finitely generated free)-by-cyclic groups and all Baumslag--Solitar groups, solving it in two cases that have been raised explicitly by Belk, Bleak, Matucci and Zaremsky. This is joint work with Kai-Uwe Bux and Xiaolei Wu.