The generation problem in the Thompson group F

Wed, 15/06/2016 - 10:30
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We show that the generation problem in the Thompson group F is decidable, i.e., there is an algorithm which decides whether a finite set of elements of F generates the whole F. The algorithm makes use of the Stallings 2-core of subgroups of F, which can be defined in an analogous way to the Stallings core of subgroups of a free group. An application of the algorithm shows that F is a cyclic extension of a group K which has a maximal elementary amenable subgroup B. The group B is a copy of a subgroup of F constructed by Brin.