{"paper":{"title":"The Conjugacy Problem for Higman's Group","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Owen Baker","submitted_at":"2019-02-16T04:09:38Z","abstract_excerpt":"In 1951, Higman constructed a remarkable group $$H=\\left\\langle a,b,c,d \\, \\left| \\, b^a = b^2, c^b = c^2, d^c = d^2, a^d = a^2 \\right. \\right\\rangle$$ and used it to produce the first examples of infinite simple groups. By studying fixed points of certain finite state transducers, we show the conjugacy problem in $H$ is decidable (for all inputs). Diekert, Laun and Ushakov have recently shown the word problem in $H$ is solvable in polynomial time, using the power circuit technology of Myasnikov, Ushakov and Won. Building on this work, we show in a strongly generic setting that the conjugacy p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06037","kind":"arxiv","version":1},"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"}