On non-surjective word maps on PSL 2(Fq)
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Dokumenter
- Fulltext
Indsendt manuskript, 144 KB, PDF-dokument
Jambor–Liebeck–O’Brien showed that there exist non-proper-power word maps which are not surjective on PSL 2(Fq) for infinitely many q. This provided the first counterexamples to a conjecture of Shalev which stated that if a two-variable word is not a proper power of a non-trivial word, then the corresponding word map is surjective on PSL 2(Fq) for all sufficiently large q. Motivated by their work, we construct new examples of these types of non-surjective word maps. As an application, we obtain non-surjective word maps on the absolute Galois group of Q , and on SL 2(K) where K is a number field of odd degree.
Originalsprog | Engelsk |
---|---|
Tidsskrift | Archiv der Mathematik |
Vol/bind | 122 |
Sider (fra-til) | 1-11 |
Antal sider | 11 |
ISSN | 0003-889X |
DOI | |
Status | Udgivet - 2024 |
Bibliografisk note
Funding Information:
We thank the anonymous reviewers for their helpful comments and suggestions. The first author wishes to thank Chen Meiri for a number of discussions on word maps. The work of the first author was supported by the ISF Grant no. 1226/19 at the Department of Mathematics at the Technion. The second author acknowledges the Initiation Grant from the Indian Institute of Science Education and Research Bhopal, and the INSPIRE Faculty Award IFA18-MA123 from the Department of Science and Technology, Government of India.
Publisher Copyright:
© 2023, Springer Nature Switzerland AG.
ID: 371023529