| Title: | The invariant of PGU(3,q) in the Hermitian function field |
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| Authors: | ID Gatti, Barbara (Author)
ID Ghiandoni, Francesco (Author)
ID Korchmáros, Gábor (Author) |
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| Files: |  ADAM_Gatti,Ghiandoni,Korchmaros_2025.pdf (388,93 KB)
MD5: 246AE0432D213D7E16F8784633368DAB
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | Let F = F|K be a function field over an algebraically closed constant field K of positive characteristic p. For a K-automorphism group G of F, the invariant of G is the fixed field FG of G. If F has transendency degree 1 (i.e. F is the function field of an irreducible curve) and FG is rational, then each generator of FG uniquely determines FG and it makes sense to call each of them the invariant of G. In this paper, F is the Hermitian function field K(Hq)=K(x,y) with yq + y − xq + 1 = 0 and q = pr. We determine the invariant of Aut(K(Hq)) \cong PGU(3,q), and discuss some related questions on Galois subcovers of maximal curves over finite fields. |
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| Keywords: | function field, finite field, automorphism group, invariant |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 26.02.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 8 str. |
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| Numbering: | Vol. 8, no. 1, [article no.] P1.09 |
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| PID: | 20.500.12556/RUP-21972  |
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| UDC: | 51 |
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| eISSN: | 2590-9770 |
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| DOI: | https://doi.org/10.26493/2590-9770.1746.53c |
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| Publication date in RUP: | 21.10.2025 |
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| Views: | 273 |
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| Downloads: | 3 |
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