Abstract
We show that the generation problem in Thompson's group F is decidable, i.e., there is an algorithm which decides if 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 finitely generated free group. Further study of the Stallings 2-core of subgroups of F provides a solution to another algorithmic problem in F. Namely, given a finitely generated subgroup H of F, it is decidable if H acts transitively 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 maximal subgroup 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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Pages (from-to) | 1-136 |
Number of pages | 136 |
Journal | Memoirs of the American Mathematical Society |
Volume | 292 |
Issue number | 1451 |
DOIs | |
State | Published - 1 Jan 2023 |
Keywords
- closed subgroups
- decision problems
- diagram groups
- directed 2-complexes
- homeomorphisms of the interval
- maximal subgroups
- the Stallings 2-core
- Thompson's group F
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics