{"paper":{"title":"On minimal non-$CL$-groups","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Daniele Ettore Otera (Universite' Paris-Sud 11, France), Francesco G. Russo (Universita' degli Studi di Palermo, Italy), Orsay cedex, Palermo","submitted_at":"2010-10-19T12:32:55Z","abstract_excerpt":"If $m$ is a positive integer or infinity, the $m$-layer (or briefly, the layer) of a group $G$ is the subgroup $G_m$ generated by all elements of $G$ of order $m$. This notion goes back to some contributions of Ya.D. Polovickii of almost 60 years ago and is often investigated, because the presence of layers influences the group structure. If $G_m$ is finite for all $m$, $G$ is called $FL$-group (or $FO$-group). A generalization is given by $CL$-groups, that is, groups in which $G_m$ is a Chernikov group for all $m$. By working on the notion of $CL$-group instead of that of $FL$-group, we exten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3876","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"}