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Plane curves given by separated polynomials are well-known and studied in the literature. However just few informations are known on their automorphism groups. In this paper we compute the full automorphism group of $\\mathcal{C}$ when $m \\not\\equiv 1 \\pmod {p^n}$ and $B(X)$ has just one root in $K$, that is $B(X)=b_m(X+"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1708.05450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-17T22:11:48Z","cross_cats_sorted":[],"title_canon_sha256":"e02cb65c18a52a297bd7420f3a17ad616385bbbfd83a84d8cef27f7ebd2a0b71","abstract_canon_sha256":"9010ed5be20ff62bceda7fecefda0721fbf16e8af7b9219cbe00836d620e8ae5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:50.024926Z","signature_b64":"8K5Zd2Afd10kucwM55ulhRBSf9wKBUl1ckuMAfWE5JW7t1qfHEf2Mt1fhqra5Hhhz++pNp9Xyb/9VSHgy9epBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a24b9b8b9702752a88693ae4042eb13c1aefb2395ec25cefbc36251233bd9e7","last_reissued_at":"2026-05-18T00:37:50.024305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:50.024305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On plane curves given by separated polynomials and their automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Giovanni Zini, Maria Montanucci, Matteo Bonini","submitted_at":"2017-08-17T22:11:48Z","abstract_excerpt":"Let $\\mathcal{C}$ be a plane curve defined over the algebraic closure $K$ of a prime finite field $\\mathbb{F}_p$ by a separated polynomial, that is $\\mathcal{C}: A(y)=B(x)$, where $A(y)$ is an additive polynomial of degree $p^n$ and the degree $m$ of $B(X)$ is coprime with $p$. Plane curves given by separated polynomials are well-known and studied in the literature. However just few informations are known on their automorphism groups. 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