{"paper":{"title":"Homotopy theory and generalized dimension subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Jie Wu, Roman Mikhailov, Sergei O. Ivanov","submitted_at":"2015-06-27T20:01:34Z","abstract_excerpt":"Let $G$ be a group and $R,S,T$ its normal subgroups. There is a natural extension of the concept of commutator subgroup for the case of three subgroups $\\|R,S,T\\|$ as well as the natural extension of the symmetric product $\\|\\bf r,\\bf s,\\bf t\\|$ for corresponding ideals $\\bf r,\\bf s, \\bf t$ in the integral group ring $\\mathbb Z[G]$. In this paper, it is shown that the generalized dimension subgroup $G\\cap (1+\\|\\bf r,\\bf s,\\bf t\\|)$ has exponent 2 modulo $\\|R,S,T\\|.$ The proof essentially uses homotopy theory. The considered generalized dimension quotient of exponent 2 is identified with a subg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08324","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"}