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5. Other problems

Everything that didn’t find a home in other sections.


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      Problem 5.1.

      [Girgorchuk] Conjecture:A finitely presented group is either virtually nilpotent, or contains a free subsemigroup of order 2.


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          Problem 5.2.

          Is there a finitely presented simple group that is not 2-generated?


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              Problem 5.3.

              Is true that every infinite amenable group contains an infinite abelian subgroup?


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                  Problem 5.4.

                  G \curvearrowright X, p, x, y \in X. What can be said on P(x \in O_\Lambda(p) \operatorname{ and } y \in O_{\Lambda}(p))? Are these events positively/negatively correlated? (Here O_\Lambda(p) is the inverted orbit of p.)


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                      Problem 5.5.

                      Is there a f.p. infinite torsion group? Conjecture:(Grigorchuk) no.


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                          Problem 5.6.

                          Is the Tarski number of G \times G equal to the Tarski number of G?


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                              Problem 5.7.

                              Is there a group with Tarski number 7?

                              If this group is amenable, the Folner function of this group is universal bound.


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                                  Problem 5.8.

                                  [Grigorchuk] Conjecture:If the Folner function of a group is sub-exponential, then the group is virtually nilpotent.


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                                      Problem 5.9.

                                      Are the Hanoi tower groups H_n, n \geq 4 amenable?

                                          Cite this as: AimPL: Amenability of discrete groups, available at http://aimpl.org/amenablediscrete.