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PreprintCC BY 4.0arXiv

Discrete hermitian groups are FC-hypercentral

  • Tron Omland
Open at sourcePDFDOICite

Abstract

We show that a discrete group is hermitian if and only if it is FC-hypercentral, that is, if and only if it does not have any nontrivial ICC quotients. In particular, a finitely generated group is hermitian if and only if it is virtually nilpotent. The main step is an elementary, self-contained proof that every hermitian ICC group is trivial, based on a finite-set separation property of nontrivial ICC groups.

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Cite

BibTeXRIS
BibTeX
@misc{omland2026discrete,
  title = {{Discrete hermitian groups are FC-hypercentral}},
  author = {Tron Omland},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40226},
  eprint = {2610.40226},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40226},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Discrete hermitian groups are FC-hypercentral
AU  - Tron Omland
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40226
UR  - https://arxiv.org/abs/2610.40226
AB  - We show that a discrete group is hermitian if and only if it is FC-hypercentral, that is, if and only if it does not have any nontrivial ICC quotients. In particular, a finitely generated group is hermitian if and only if it is virtually nilpotent. The main step is an elementary, self-contained proof that every hermitian ICC group is trivial, based on a finite-set separation property of nontrivial ICC groups.
ER  -