On the length of nonsolutions to equations with constants in some linear groups
Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung
Beitragende
Abstract
We show that for any finite-rank–free group (Formula presented.), any word-equation in one variable of length (Formula presented.) with constants in (Formula presented.) fails to be satisfied by some element of (Formula presented.) of word-length (Formula presented.). By a result of the first author, this logarithmic bound cannot be improved upon for any finitely generated group (Formula presented.). Beyond free groups, our method (and the logarithmic bound) applies to a class of groups including (Formula presented.) for all (Formula presented.), and the fundamental groups of all closed hyperbolic surfaces and 3-manifolds. Finally, using a construction of Nekrashevych, we exhibit a finitely generated group (Formula presented.) and a sequence of word-equations with constants in (Formula presented.) for which every nonsolution in (Formula presented.) is of word-length strictly greater than logarithmic.
Details
Originalsprache | Englisch |
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Seiten (von - bis) | 2338-2349 |
Seitenumfang | 12 |
Fachzeitschrift | Bulletin of the London Mathematical Society |
Jahrgang | 56 |
Ausgabenummer | 7 |
Publikationsstatus | Veröffentlicht - Juli 2024 |
Peer-Review-Status | Ja |
Externe IDs
ORCID | /0000-0002-7245-2861/work/173514038 |
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