Abstract
ABSTRACTLet 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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