On non-surjective word maps on PSL 2(Fq)

Research output: Contribution to journalJournal articleResearchpeer-review


  • Fulltext

    Submitted manuscript, 144 KB, PDF document

  • Arindam Biswas
  • Jyoti Prakash Saha

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.

Original languageEnglish
JournalArchiv der Mathematik
Pages (from-to)1-11
Number of pages11
Publication statusPublished - 2024

Bibliographical note

Publisher Copyright:
© 2023, Springer Nature Switzerland AG.

    Research areas

  • Finite simple groups, Galois groups, Word maps

ID: 371023529