Kazhdan quotients of Golod-Shafarevich groups

Abstract

The main goal of this paper is to prove that every Golod-Shafarevich group has an infinite quotient with Kazhdan's property $(T)$. In particular, this gives an affirmative answer to the well-known question about non-amenability of Golod-Shafarevich groups.

arXiv comment38 pages, final preprint version (slightly different from the published version)

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