An alternative proof of Kazhdan property for elementary groups

Abstract

In 2010, Invent. Math., Ershov and Jaikin-Zapirain proved Kazhdan's property (T) for elementary groups. This expository article focuses on presenting an alternative simpler proof of that. Unlike the original one, our proof supplies no estimate of Kazhdan constants. It may be regarded as a specific example of the results in the paper "Upgrading fixed points without bounded generation" (arXiv:1505.06728, forthcoming version) by the author.

9 pages (v2), terminology and symbols are changed according to progress of arXiv:1505.06728 (in v3, forthcoming version); 8 pages, this is an expository article to describe a specific case of the paper (arXiv:1505.06728) by the author. Submitted as a manuscript for conference proceedings