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Title:Compactness of the space of marked groups and examples of L2-Betti numbers of simple groups
Author(s):Zhu, Kejia
Advisor(s):Mineyev, Igor
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:M.S.
Genre:Thesis
Subject(s):Geometric group theory
Topology
Abstract:This paper contains two parts. The first part will introduce Gn space and will show its compact. I will give two proofs for the compactness, the first one is due to Rostislav Grigorchuk [1], which refers to geometrical group theory and after the first proof I will give a more topological proof. In the second part, our goal is to prove a theorem by Denis Osin and Andreas Thom [2]: for every integer n ≥ 2 and every ε ≥ 0 there exists an infinite simple group Q generated by n elements such that β(2)(Q) ≥ n − 1 − ε. As a corollary, we can prove that for every positive integer n 1 there exists a simple group Q with d(Q) = n. In the proof of this theorem, I added the details to the original proof. Moreover, I found and fixed an error of the original proof in [2], although it doesn’t affect the final result.
Issue Date:2017-03-28
Type:Thesis
URI:http://hdl.handle.net/2142/97234
Rights Information:Copyright 2017 Kejia Zhu
Date Available in IDEALS:2017-08-10
Date Deposited:2017-05


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