Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 32 min ago
PreprintCC BY 4.0arXiv

Subgroup and Submonoid Membership in the lampshuffler of ℤ

  • Corentin Bodart
  • Ruiwen Dong
Open at sourcePDFDOICite

Abstract

The lampshuffler group of ℤ is the semidirect product FSym(ℤ) rtimes ℤ, which consists of all permutations of ℤ that act as a translation outside a finite set. This infinite permutation group naturally contains as subgroups the wreath products H wr ℤ for every finite group H. We prove that the Subgroup Membership Problem, and more generally, the Submonoid Membership Problem, are decidable in FSym(ℤ) rtimes ℤ. Our proof reduces Subgroup and Submonoid Membership in FSym(ℤ) rtimes ℤ to Subgroup Membership in the wreath products H wr ℤ, which was shown to be decidable by Lohrey, Steinberg and Zetzsche (2015).

Related

  1. Standard bases for shift-stable groups and Subgroup Membership in wreath products
    Ruiwen Dong
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Unifying Data-Adaptive Longitudinal Treatment-Effect Subgroup Discovery and Pretreatment Membership Prediction
    Pu Zhang, Yuheng Li, Jiakun Jiang
    arXivPreprintCC0Full textStatisticsarXiv
  3. A Nica-amenable submonoid of a group which fails to embed in an amenable group
    Adam Dor-On, Boyu Li
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Schatten class membership of products of composition operators and their adjoints
    Qianrui Leng, Xianfeng Zhao
    arXivPreprintCC0Full textAnalysis & PDEsarXiv
  5. A Nearly Quadratic Lower Bound for Linear Optimization over Convex Bodies in the Membership Oracle Model
    Santosh S. Vempala
    arXivPreprintarXiv licenceFull textAnalysis & PDEsOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@misc{bodart2026subgroup,
  title = {{Subgroup and Submonoid Membership in the lampshuffler of $\mathbbZ$}},
  author = {Corentin Bodart and Ruiwen Dong},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06108},
  eprint = {2610.06108},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06108},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Subgroup and Submonoid Membership in the lampshuffler of ℤ
AU  - Corentin Bodart
AU  - Ruiwen Dong
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06108
UR  - https://arxiv.org/abs/2610.06108
AB  - The lampshuffler group of ℤ is the semidirect product FSym(ℤ) rtimes ℤ, which consists of all permutations of ℤ that act as a translation outside a finite set. This infinite permutation group naturally contains as subgroups the wreath products H wr ℤ for every finite group H. We prove that the Subgroup Membership Problem, and more generally, the Submonoid Membership Problem, are decidable in FSym(ℤ) rtimes ℤ. Our proof reduces Subgroup and Submonoid Membership in FSym(ℤ) rtimes ℤ to Subgroup Membership in the wreath products H wr ℤ, which was shown to be decidable by Lohrey, Steinberg and Zetzsche (2015).
ER  -