The Generation Problem in Thompson Group $F$
Seiten
2024
American Mathematical Society (Verlag)
978-1-4704-6723-4 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-6723-4 (ISBN)
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.
Gili Golan Polak, Ben Gurion University of the Negev, Be'er Sheva, Israel.
| Erscheinungsdatum | 02.02.2024 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 272 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-6723-2 / 1470467232 |
| ISBN-13 | 978-1-4704-6723-4 / 9781470467234 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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