Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Does there exist a non trivial homomorphism from Thompson's group T to a linear group?

share|improve this question
    
... where a "linear group" is a group of automorphisms of a finite dimensional vector space, or over a finitely generated module? $\:$ In the latter case, what if any, are the restrictions on the ring of scalars? $\;\;\;$ –  Ricky Demer Apr 19 '13 at 4:18
    
By a linear group, I mean $GL_n(\mathbb{R})$. –  Mahdi Teymuri Garakani Apr 19 '13 at 4:31
2  
Actually, instead of ${\mathbb R}$, you can use any field. –  Misha Apr 19 '13 at 14:00
    
Thanks Misha for the comment. –  Mahdi Teymuri Garakani Apr 19 '13 at 14:42
add comment

1 Answer

up vote 11 down vote accepted

No: T is infinite, finitely presented and simple. Fg linear groups are residually finite, by Mal'cev's theorem. QED.

share|improve this answer
    
Thanks for the answer. –  Mahdi Teymuri Garakani Apr 19 '13 at 14:45
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.