Let $GL_n$ be the group of all $n$ by $n$ invertible matrices. Why the finite subgroups of $GL_n$ is closed with respect to Zariski topology? Are the zeros defined by some equations? Thank you very much.
Asked
Active
Viewed 114 times
2
-
3Any finite subset of an affine variety is closed. – Tobias Kildetoft Sep 25 '13 at 11:36
-
A single point is closed (=the zero set of linear polynomials of the form $x_i-a_i$) => any finite set is closed – Jyrki Lahtonen Sep 25 '13 at 11:49
-
@JyrkiLahtonen, thank you very much. But the points of $GL_n$ are matrices. What are the polynomial equations in this case? – LJR Sep 25 '13 at 11:51
-
2Do you know how $GL_n$ has been identified with a variety in the first place? – Tobias Kildetoft Sep 25 '13 at 11:56
-
$x_{ij}-a_{ij}$ – Jyrki Lahtonen Sep 25 '13 at 12:31