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3. Thompson groups

    1. Commutator width of Thompson groups

          Let $G$ be $F,T$ or $V$ or a topological full group. Let $\rho_1(g)$ be the commutator width of $g$ and $\rho_2(g)$ the minimum number of involutions in a factorization of $g$.

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      Problem 3.1.

      1. Prove that $\rho_1$ and $\rho_2$ are bounded
      2. Prove that $\rho_1 = 1$ and $\rho_2 = 3$
      3. Is there a finitely presented simple group with commutator width greater or equal to $2$?

        • Maximal subgroups in Thompson groups


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          Problem 3.2.

          Find new maximal subgroups of infinite index in Thompson groups

              Cite this as: AimPL: Groups of dynamical origin, available at http://aimpl.org/groupdynamorigin.