A dynamical definition of f.g. virtually free groups

作者：Bennett Daniel^*; Bleak Collin^*

来源：International Journal of Algebra and Computation, 2016, 26(1): 105-121.

DOI：10.1142/S0218196716500053

• CoCF groups
• Thompson groups
• Lehnert's conjecture
• group actions
• geometric actions

We show that the class of finitely generated virtually free groups is precisely the class of finitely generated demonstrable subgroups for Thompson's group V. The class of demonstrable groups for V consists of all groups which can embed into V with a natural dynamical behavior in their induced actions on the Cantor space C-2 := {0, 1}(omega). There are also connections with formal language theory, as the class of groups with context-free word problem is also the class of finitely generated virtually free groups, while Thompson's group V is a candidate as a universal coCF group by Lehnert's conjecture, corresponding to the class of groups with context free co-word problem (as introduced by Holt, Rees, Rover, and Thomas). Our main results answers a question of Berns-Zieve, Fry, Gillings, Hoganson, and Matthews, and separately of Bleak and Salazar-Diaz, and it fits into the larger exploration of the class of coCF groups as it shows that all four of the known closure properties of the class of coCF groups hold for the set of finitely generated subgroups of V.

• 出版日期2016-2