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

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... 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
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
up vote 12 down vote accepted

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

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Thanks for the answer. – Mahdi Teymuri Garakani Apr 19 '13 at 14:45

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