{
  "abstract": "Let $G$ be a group and $K$ be a normal subgroup of $G$. A sequence over $G$ is a finite collection of terms from $G$, where repetition is allowed, and the order is disregarded. A product-$K$ sequence is a sequence whose terms can be ordered such that their product in $G$ belongs to $K$. The set $\\mathcal B_K (G)$ of all product-$K$ sequences over $G$ forms a monoid, called the monoid of product-$K$ sequences, under the operation of sequence concatenation. In this paper, we investigate the algebraic and arithmetic properties of the monoid $\\mathcal B_K (G)$. Among our main results, we provide precise characterizations of when $\\mathcal B_K (G)$ satisfies key properties, namely being (transfer) Krull, a (seminormal) C-monoid, or (half-)factorial. After that, we study the Isomorphism Problem for monoids of product-$K$ sequences. Our results generalize existing frameworks, making them applicable to both the classical abelian and the more recently developed non-abelian settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.03020",
  "author_total": 2,
  "authors": [
    {
      "name": "Jun Seok Oh"
    },
    {
      "name": "Doniyor Yazdonov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dshng53egyshz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.03020",
  "fulltext_url": null,
  "id": "dshng53egyshz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.03020",
  "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.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7167623634",
  "pdf_url": "https://arxiv.org/pdf/2607.03020",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dshng53egyshz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2607.03020",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.03020"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On algebraic and arithmetic properties of monoids of product-$K$ sequences",
  "title_text": "On algebraic and arithmetic properties of monoids of product-K sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/dshng53egyshz",
  "venue": "arXiv",
  "versions": []
}