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arXiv · 2610.40226

Discrete hermitian groups are FC-hypercentral

Tron Omland
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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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Tron Omland. 2026-10-29. Discrete hermitian groups are FC-hypercentral. https://arxiv.org/abs/2610.40226

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