English

On the permanence properties of residually exact groups

Group Theory 2025-12-16 v1 Operator Algebras

Abstract

A discrete group Γ\Gamma is called exact if the reduced group C*-algebra Cλ(Γ){C_{\lambda}}^{*}(\Gamma) is exact as C*-algebras, and a discrete group Λ\Lambda is called residually exact if every nonunital element gΛg \in \Lambda admits a surjective group homomorphism from Λ\Lambda to some exact group Γ\Gamma which maps gg to a nonunital element of Γ\Gamma. We prove the class of residually exact groups is closed under taking Green's graph products [1], double amalgamed products and special HNN extensions.

Keywords

Cite

@article{arxiv.2512.13212,
  title  = {On the permanence properties of residually exact groups},
  author = {Hikaru Awazu},
  journal= {arXiv preprint arXiv:2512.13212},
  year   = {2025}
}

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Written in Jan. 2020