Year: 2026
Type: article
Abstract: In 2016 Tafazolian et al. [31] introduced new families of $$\mathbb {F}_{q^{2n}}$$ F q 2 n -maximal function fields $$\mathcal {Y}_{n,s}$$ Y n , s and $$\mathcal {X}_{n,s,a,b}$$ X n , s , a , b arising as subfields of the first generalized GK function field (GGS). In this way the authors found new examples of maximal function fields that are not isomorphic to subfields of the Hermitian function field. In this paper we construct analogous function fields $$\tilde{\mathcal {Y}}_{n,s}$$ Y ~ n , s and $$\tilde{\mathcal {X}}_{n,s,a,b}$$ X ~ n , s , a , b as subfields of the second generalized GK function field (BM) and determine their automorphism groups. Using that the automorphism group is an invariant under isomorphism, we show that the function fields $$\tilde{\mathcal {Y}}_{n,s}$$ Y ~ n , s and $${\mathcal {Y}}_{n,s}$$ Y n , s , as well as $$\tilde{\mathcal {X}}_{n,s,a,b}$$ X ~ n , s , a , b and $$\mathcal {X}_{n,s,a,b}$$ X n , s , a , b , are not isomorphic unless m / s divides $$q^2-q+1$$ q 2 - q + 1 and 3 divides n . In other words, the difference between the BM and GGS function fields can be found again at the level of the subfields that we consider.
Source: Research in Number Theory
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,590
Award: G2419008608
OpenAlex ID: W7131782840