{"paper":{"title":"On lengths of HZ-localization towers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Roman Mikhailov, Sergei O. Ivanov","submitted_at":"2016-05-26T09:04:49Z","abstract_excerpt":"In this paper, the $H\\mathbb Z$-length of different groups is studied. By definition, this is the length of $H\\mathbb Z$-localization tower or the length of transfinite lower central series of $H\\mathbb Z$-localization. It is proved that, for a free noncyclic group, its $H\\mathbb Z$-length is $\\geq \\omega+2$. For a large class of $\\mathbb Z[C]$-modules $M,$ where $C$ is an infinite cyclic group, it is proved that the $H\\mathbb Z$-length of the semi-direct product $M\\rtimes C$ is $\\leq \\omega+1$ and its $H\\mathbb Z$-localization can be described as a central extension of its pro-nilpotent compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08198","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"}