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PreprintCC BY 4.0arXiv

PHP decompositions and primitivity of group rings for linear groups

  • Felipe I. Flores
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Abstract

We show that every countable group G that has Ozawa's property PHP and contains a non-abelian free subgroup has the following property: the group ring KG is primitive for any field K. As a consequence, we deduce that all non-trivial countable linear groups with trivial amenable radical have this property. Along the way, we prove that the class of groups with PHP enjoys some permanence properties that are of independent interest.

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Cite

BibTeXRIS
BibTeX
@misc{flores2026decompositions,
  title = {{PHP decompositions and primitivity of group rings for linear groups}},
  author = {Felipe I. Flores},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14814},
  eprint = {2609.14814},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14814},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - PHP decompositions and primitivity of group rings for linear groups
AU  - Felipe I. Flores
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14814
UR  - https://arxiv.org/abs/2609.14814
AB  - We show that every countable group G that has Ozawa's property PHP and contains a non-abelian free subgroup has the following property: the group ring KG is primitive for any field K. As a consequence, we deduce that all non-trivial countable linear groups with trivial amenable radical have this property. Along the way, we prove that the class of groups with PHP enjoys some permanence properties that are of independent interest.
ER  -