The Tits alternative

Author(s)

Renan Campos Gutierrez

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2012-06-20

Examining board members

Daniel Levcovitz; Jairo Zacarias Goncalves; Eduardo Tengan

• Advisor: Daniel Levcovitz

Abstract

This masters project aims to give an elementary proof of the following theorem of Tits, known as the Alternative Tits Theorem: Let G be a finitely generated linear group over a field. Then either G is solvable by finite or G contains a noncyclic free subgroup. This theorem was proved by J. Tits in 1972 [4], was considered by the mathematician J.P. Serre, as one of the most important algebra results of the XX century. When we say an elementary proof, we absolutely not mean a simple proof. We will follow the simplified proof of John D. Dixon (AU)

• FAPESP's process: 09/12335-1 - Tits' Alternative Theorem
• Grantee: Renan Campos Gutierrez
• Support Opportunities: Scholarships in Brazil - Master