what is the order of group GL2(R), where all the entries of the group are integers mod p, where p is prime.

Question

Welcome to Math.SE. What have you tried so far ? Where are you stuck ? — Shailesh, Jun 28 '18 at 05:33
Shouldn't this be denoted $\operatorname{GL}_2(\mathbb{Z}/p\mathbb{Z})$ or $\operatorname{GL}_2(\mathbb{F}_p)$ instead? — Suzet, Jun 28 '18 at 05:33
I also support the opinion of other voters that this question is missing context and other relevant pieces. — Jyrki Lahtonen, Jun 28 '18 at 12:22

score 0 · Answer 1 · edited May 16 '22 at 22:13

0

That's $GL_2(\Bbb Z/p\Bbb Z)$. The first column vector must be non-zero, zthe second must not be in the subspace spanned by the first vector. This gives us $p^2-1$ choices for the first column and $p^2-p$ for the second. We conclude $\|GL_2(\Bbb Z/p\Bbb Z)=(p^2-1)(p^2-p)$,

edited May 16 '22 at 22:13

Jean Marie

81,803

answered Jun 28 '18 at 05:33

Hagen von Eitzen

374,180

3

You mean $(p^2-1)(p^2-p)$. – Angina Seng Jun 28 '18 at 06:32

what is the order of group GL2(R), where all the entries of the group are integers mod p, where p is prime.

1 Answers1