{
  "abstract": "Let $P$ be a group, $L(P)$ be the free multiplicative Lie algebra with normal subgroup $Γ_n(P)$ generated by Lie bracket ``commutators'' of weight $n$ and $\\{ γ_n(P) \\}$ be the lower central series of $P$. We prove that $Γ_n(P) \\simeq γ_n(P)$ for arbitrary $n \\geq 1$ and $P$ a finitely generated parafree group such that $H_2(P, \\mathbb{Z}) = 0 = H_3(P, \\mathbb{Z})$ (e.g. $P$ satisfies the Strong Parafree Conjecture), in particular Ellis's conjecture holds i.e. the above isomorphism holds for finitely generated free group $P$ but this easily implies it holds for any free group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19595",
  "author_total": 1,
  "authors": [
    {
      "name": "Dessislava H. Kochloukova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0f0f70zeqxrm1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19595",
  "fulltext_url": null,
  "id": "0f0f70zeqxrm1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19595",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7213601553",
  "pdf_url": "https://arxiv.org/pdf/2609.19595",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0f0f70zeqxrm1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19595",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19595"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The free multiplicative Lie algebra $L(P)$ for a finitely generated parafree group $P$",
  "title_text": "The free multiplicative Lie algebra L(P) for a finitely generated parafree group P",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/0f0f70zeqxrm1",
  "venue": "arXiv",
  "versions": []
}