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On algebraic and arithmetic properties of monoids of product-K sequences

  • Jun Seok Oh
  • Doniyor Yazdonov
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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 ℬK (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 ℬK (G). Among our main results, we provide precise characterizations of when ℬK (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.

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Cite

BibTeXRIS
BibTeX
@misc{oh2026algebraic,
  title = {{On algebraic and arithmetic properties of monoids of product-$K$ sequences}},
  author = {Jun Seok Oh and Doniyor Yazdonov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.03020},
  eprint = {2607.03020},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.03020},
}
RIS
TY  - UNPB
TI  - On algebraic and arithmetic properties of monoids of product-K sequences
AU  - Jun Seok Oh
AU  - Doniyor Yazdonov
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2607.03020
UR  - https://arxiv.org/abs/2607.03020
AB  - 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 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 ℬ_K (G). Among our main results, we provide precise characterizations of when 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.
ER  -