Return to Question

added 45 characters in body

view source

edited Jul 14 2011 at 12:07

Are there some nontrivial group homomorphisms from $SL_n(\mathbb{Z})$ to $GL_{n-1}(\mathbb{Z})$ for $n\geq3$ except the determinant? Or This should be a natural question and any references are welcomed.

PS. A similar question has the answer 'NO' for a finite field $F_p$ instead of $\mathbb{Z}$? This should be a natural question and any references are welcomed\mathbb{Z}$ as explained below.

added 23 characters in body

view source

edited Jul 14 2011 at 11:09

yeshengkui
883●3●11

Are there some nontrivial group homomorphisms from $SL_n(\mathbb{Z})$ to $GL_{n-1}(\mathbb{Z})$ for $n\geq3$? n\geq3$ except the determinant? Or a similar question for a finite field $F_p$ instead of $\mathbb{Z}$? This should be a natural question and any references are welcomed.

view source

asked Jul 14 2011 at 10:15

yeshengkui
883●3●11

Are there some nontrivial group homomorphisms from $SL_n(\mathbb{Z})$ to $GL_{n-1}(\mathbb{Z})$ for $n\geq3$?

Are there some nontrivial group homomorphisms from $SL_n(\mathbb{Z})$ to $GL_{n-1}(\mathbb{Z})$ for $n\geq3$? Or a similar question for a finite field $F_p$ instead of $\mathbb{Z}$? This should be a natural question and any references are welcomed.