{"paper":{"title":"On finite groups in which coprime commutators are covered by few cyclic subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Cristina Acciarri, Pavel Shumyatsky","submitted_at":"2013-11-24T17:49:27Z","abstract_excerpt":"The coprime commutators $\\gamma_j^*$ and $\\delta_j^*$ were recently introduced as a tool to study properties of finite groups that can be expressed in terms of commutators of elements of coprime orders. They are defined as follows. Let $G$ be a finite group. Every element of $G$ is both a $\\gamma_1^*$-commutator and a $\\delta_0^*$-commutator. Now let $j\\geq 2$ and let $X$ be the set of all elements of $G$ that are powers of $\\gamma_{j-1}^*$-commutators. An element $g$ is a $\\gamma_j^*$-commutator if there exist $a\\in X$ and $b\\in G$ such that $g=[a,b]$ and $(|a|,|b|)=1$. For $j\\geq 1$ let $Y$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6148","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"}