{"paper":{"title":"Free groups and automorphism groups of infinite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Philipp L\\\"ucke, Saharon Shelah","submitted_at":"2012-11-29T11:58:41Z","abstract_excerpt":"Let \\lambda be a cardinal with \\lambda=\\lambda^{\\aleph_0} and p be either 0 or a prime number. We show that there are fields K_0 and K_1 of cardinality \\lambda and characteristic p such that the automorphism group of K_0 is a free group of cardinality 2^\\lambda and the automorphism group of K_1 is a free abelian group of cardinality 2^\\lambda. This partially answers a question from [8] and complements results from [15], [16] and [17]. The methods developed in the proof of the above statement also allow us to show that the above cardinal arithmetic assumption is consistently not necessary for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6891","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}