## Abstract

We show that the generation problem in Thompson’s group

is an algorithm which decides if a finite set of elements of

algorithm makes use of the Stallings 2-core of subgroups of

analogous way to the Stallings core of subgroups of a finitely generated free group. Further

study of the Stallings 2-core of subgroups of

problem in

transitively on the set of finite dyadic fractions D. Other applications of the study include

the construction of new maximal subgroups of

subgroup of infinite index which acts transitively on the set D and the construction of an

elementary amenable subgroup of

*F*is decidable, i.e., thereis an algorithm which decides if a finite set of elements of

*F*generates the whole*F*. Thealgorithm makes use of the Stallings 2-core of subgroups of

*F*, which can be defined in ananalogous way to the Stallings core of subgroups of a finitely generated free group. Further

study of the Stallings 2-core of subgroups of

*F*provides a solution to another algorithmicproblem in

*F*. Namely, given a finitely generated subgroup H of F, it is decidable if H actstransitively on the set of finite dyadic fractions D. Other applications of the study include

the construction of new maximal subgroups of

*F*of infinite index, among which, a maximalsubgroup of infinite index which acts transitively on the set D and the construction of an

elementary amenable subgroup of

*F*which is maximal in a normal subgroup of*F*.Original language | English |
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State | Published - 2016 |

### Publication series

Name | Arxiv preprint |
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## Keywords

- math.GR

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