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According to their result, many fake projective planes admit a nontrivial group of automorphisms, and in that case it is isomorphic to $\\bbZ/3\\bbZ$, $\\bbZ/7\\bbZ$, $7:3$, or $(\\bbZ/3\\bbZ)^2$, where $7:3$ is the unique non-abelian group of order 21.\n  Let $G$ be a group of automorphisms of a fake projective plane $X$. In this paper we classify all possible structures of the quotient surface $X/G$ and its minimal resolution."},"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":"0802.3435","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-02-23T09:56:25Z","cross_cats_sorted":[],"title_canon_sha256":"ae9cebd967b20675f48399f30b602cfdc10ca26ef6886d917fc0a0fd8b8378c2","abstract_canon_sha256":"a0aee288a135ac708c613b88a987b42d3e9cd2e05b17b1418e4d4064e2f2069a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:19.189259Z","signature_b64":"n/52umggdMRtA7qoEUiPredGEjmg8u/w3n15i6Y+SundcCs50CRnoNKe8+oT/bzuxv7OE5e5svHd8lpQq4TAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e764fa785afef32fd21d79d5f7fd95c55f49acc2e344014cff74e8f31ca08a92","last_reissued_at":"2026-05-18T02:38:19.188770Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:19.188770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quotients of fake projective planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"JongHae Keum","submitted_at":"2008-02-23T09:56:25Z","abstract_excerpt":"Recently, Prasad and Yeung classified all possible fundamental groups of fake projective planes. 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