Non-MF groups and non-finite full group C*-algebras

Abstract

Let $\Gamma$ be a property (T) group admitting an injective, non-surjective endomorphism and let $G$ be the associated ascending HNN-extension. Let $W=\left({⨁}_{G/\Gamma }\mathbb{Z}/2\mathbb{Z}\right)⋊G.$ We show that $W$ is not an MF group and that $C^{\ast }(G)$ is not a finite C*-algebra. The ideas and proofs were generated by ChatGPT 5.6 Sol, we have only refined their arguments in a hopefully more palatable form.

7 pages. The ideas and proofs were generated by ChatGPT 5.6 Sol, we have only refined their arguments in a hopefully more palatable form