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

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On non-surjective word maps on PSL 2(Fq). / Biswas, Arindam; Saha, Jyoti Prakash.

In: Archiv der Mathematik, Vol. 122, 2024, p. 1-11.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Biswas, A & Saha, JP 2024, 'On non-surjective word maps on PSL 2(Fq)', Archiv der Mathematik, vol. 122, pp. 1-11. https://doi.org/10.1007/s00013-023-01917-3

APA

Biswas, A., & Saha, J. P. (2024). On non-surjective word maps on PSL 2(Fq). Archiv der Mathematik, 122, 1-11. https://doi.org/10.1007/s00013-023-01917-3

Vancouver

Biswas A, Saha JP. On non-surjective word maps on PSL 2(Fq). Archiv der Mathematik. 2024;122:1-11. https://doi.org/10.1007/s00013-023-01917-3

Author

Biswas, Arindam ; Saha, Jyoti Prakash. / On non-surjective word maps on PSL 2(Fq). In: Archiv der Mathematik. 2024 ; Vol. 122. pp. 1-11.

Bibtex

@article{d4b01fa9efb64b899211ba058e8df715,
title = "On non-surjective word maps on PSL 2(Fq)",
abstract = "Jambor–Liebeck–O{\textquoteright}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.",
keywords = "Finite simple groups, Galois groups, Word maps",
author = "Arindam Biswas and Saha, {Jyoti Prakash}",
note = "Publisher Copyright: {\textcopyright} 2023, Springer Nature Switzerland AG.",
year = "2024",
doi = "10.1007/s00013-023-01917-3",
language = "English",
volume = "122",
pages = "1--11",
journal = "Archiv der Mathematik",
issn = "0003-889X",
publisher = "Springer Basel AG",

}

RIS

TY - JOUR

T1 - On non-surjective word maps on PSL 2(Fq)

AU - Biswas, Arindam

AU - Saha, Jyoti Prakash

N1 - Publisher Copyright: © 2023, Springer Nature Switzerland AG.

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

KW - Finite simple groups

KW - Galois groups

KW - Word maps

U2 - 10.1007/s00013-023-01917-3

DO - 10.1007/s00013-023-01917-3

M3 - Journal article

AN - SCOPUS:85173746926

VL - 122

SP - 1

EP - 11

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

ER -

ID: 371023529