## Help! Interesting Group Problem

Forum for the GRE subject test in mathematics.
mobius70
Posts: 19
Joined: Thu Jan 24, 2008 1:11 am

### Help! Interesting Group Problem

Hi

Let G be the set of all 2X2 matrices such that it's elements are integers modulo p, p is a prime number.
Determinant of matrix is not zero.
It is given that G forms a non-abelian finite group.

The question is for any prime p, what is the order of G.
e.g. in special case of p = 3 , order is 48.

If it helps, this is problem # 2.2.9 from Topics in Algebra (Herstein book second edition).

lime
Posts: 129
Joined: Tue Dec 04, 2007 2:11 am
Hi Mobius! Nice to see the person in the middle of the hot summer, preparing for autumn tests.

We actually already have solved this problem before (problem 5).

diman
Posts: 2
Joined: Tue Jul 15, 2008 7:33 am
Hi, guys
It looks like I’ll need math GRE to improve my resume ) if I have any questions would you mind to help me?
my math' background is on russian, so I'll have to start from the very begining

mathsubboy
Posts: 11
Joined: Sun Jul 20, 2008 12:11 pm

you are welcome!