Discrete hermitian groups are FC-hypercentral

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.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.40226
Primary Topic
Advanced Operator Algebra Research
Type
preprint
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preprint

Discrete hermitian groups are FC-hypercentral

Tron Omland
arXiv (Cornell University)
Advanced Operator Algebra Research
preprint

Discrete hermitian groups are FC-hypercentral

Tron Omland
preprint en

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.

arXiv (Cornell University)
Advanced Operator Algebra Research
DOIOpen Access PDFOpenAlex
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Discrete hermitian groups are FC-hypercentral — Tron Omland · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS