Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 16 min ago
PreprintarXiv licencearXiv

CSX-groups and free constructions

  • Omar Al-Raisi
  • Mohammad Shahryari
Open at sourcePDFDOICite

Abstract

Let X be a variety of groups. A group G is CSX if its maximal X-subgroups are malnormal. We prove that the amalgamated free product of two CSX-groups with a malnormal amalgam and without any involutions is again CSX. Using this, we describe conditions under which the HNN-extension of a CSX-group is CSX.

Related

  1. Sunflower-Free Uniform Families: Recursive Constructions and Explicit Bounds
    Edward Axante, Cristian Budala, David Chitic +2
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  2. The theory of nonabelian free groups has no model companion
    Olga Kharlampovich, Rizos Sklinos
    arXivPreprintarXiv licenceFull textAlgebra & number theoryLogic & foundationsarXiv
  3. Finite index rigidity of free-by-cyclic groups
    Radhika Gupta, Nir Lazarovich
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Dihedral groups of square-free order are DCI-groups
    István Kovács, Gábor Somlai
    Algebraic CombinatoricsPeer-reviewedCC BY 4.0Full textCombinatorics & discrete mathematicsCrossref
  5. Infinite free pro-p products as absolute Galois groups
    Tamar Bar-On
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{alraisi2026csxgroups,
  title = {{$\mathrmCS\mathfrakX$-groups and free constructions}},
  author = {Omar Al-Raisi and Mohammad Shahryari},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17954},
  eprint = {2610.17954},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17954},
}
RIS
TY  - UNPB
TI  - CSX-groups and free constructions
AU  - Omar Al-Raisi
AU  - Mohammad Shahryari
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.17954
UR  - https://arxiv.org/abs/2610.17954
AB  - Let X be a variety of groups. A group G is CSX if its maximal X-subgroups are malnormal. We prove that the amalgamated free product of two CSX-groups with a malnormal amalgam and without any involutions is again CSX. Using this, we describe conditions under which the HNN-extension of a CSX-group is CSX.
ER  -