On generalizations of Fermat curves over finite fields and their automorphisms |
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| Authors: | Nazar Arakelian Pietro Speziali |
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| Affiliation: | 1. CMCC, Universidade Federal do ABC, Santo André, Braziln.arakelian@ufabc.edu.br;3. Dipartamento di Matematica, Informatica ed Economia, Univesità Degli Studi della Basilicata, Potenza, Italy |
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| Abstract: | Let 𝒳 be an irreducible algebraic curve defined over a finite field 𝔽q of characteristic p>2. Assume that the 𝔽q-automorphism group of 𝒳 admits a subgroup isomorphic to the direct product of two cyclic groups Cm and Cn of orders m and n prime to p, such that both quotient curves 𝒳∕Cn and 𝒳∕Cm are rational. In this paper, we provide a complete classification of such curves as well as a characterization of their full automorphism groups. |
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| Keywords: | Algebraic curves automorphism groups finite fields |
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