{"paper":{"title":"Verbal width in anabelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Nikolay Nikolov","submitted_at":"2014-01-15T11:47:02Z","abstract_excerpt":"The class $A$ of anabelian groups is defined as the collection of finite groups without abelian composition factors. We prove that the commutator word $[x_1,x_2]$ and the power word $x_1^p$ have bounded width in $A$ when $p$ is an odd integer. By contrast the word $x^{30}$ does not have bounded width in $A$. On the other hand any given word $w$ has bounded width for those groups in $A$ whose composition factors are sufficiently large as a function of $w$. In the course of the proof we establish that sufficiently large almost simple groups cannot satisfy $w$ as a coset identity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3552","kind":"arxiv","version":2},"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"}