{"paper":{"title":"On pro-$p$ analogues of limit groups via extensions of centralizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Dessislava H. Kochloukova, Pavel A. Zalesskii","submitted_at":"2011-07-12T15:57:56Z","abstract_excerpt":"We begin a study of a pro-$p$ analogue of limit groups via extensions of centralizers and call $\\mathcal{L}$ this new class of pro-$p$ groups. We show that the pro-$p$ groups of $\\mathcal{L}$ have finite cohomological dimension, type $FP_{\\infty}$ and non-positive Euler characteristic. Among the group theoretic properties it is proved that they are free-by-(torsion-free poly -procyclic) and if non-abelian do not have a finitely generated non-trivial normal subgroup of infinite index. Furthermore it is shown that every 2 generated pro-$p$ group in the class $\\mathcal{L}$ is either free pro-$p$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2331","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"}