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Split Frobenius Groups, Equational Domains, XT- and CSX-groups

  • Omar Al-Raisi
  • Mohammad Shahryari
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Abstract

We investigate conditions under which a semidirect product G=HN, and in particular a restricted wreath product, is an equational domain. For a variety of groups X, we study semidirect products of XT-groups (groups where ⟨ A, B⟩ ∈X for any two X-subgroups A and B with nontrivial intersection) and CSX-groups (groups where all maximal X-subgroups are malnormal). We pay particular attention to split Frobenius groups and investigate conditions under which such groups are XT- or CSX-groups.

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Cite

BibTeXRIS
BibTeX
@misc{alraisi2026split,
  title = {{Split Frobenius Groups, Equational Domains, $\mathfrakXT$- and $CS\mathfrakX$-groups}},
  author = {Omar Al-Raisi and Mohammad Shahryari},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32643},
  eprint = {2610.32643},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32643},
}
RIS
TY  - UNPB
TI  - Split Frobenius Groups, Equational Domains, XT- and CSX-groups
AU  - Omar Al-Raisi
AU  - Mohammad Shahryari
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32643
UR  - https://arxiv.org/abs/2610.32643
AB  - We investigate conditions under which a semidirect product G=HN, and in particular a restricted wreath product, is an equational domain. For a variety of groups X, we study semidirect products of XT-groups (groups where ⟨ A, B⟩ ∈X for any two X-subgroups A and B with nontrivial intersection) and CSX-groups (groups where all maximal X-subgroups are malnormal). We pay particular attention to split Frobenius groups and investigate conditions under which such groups are XT- or CSX-groups.
ER  -