Help! Interesting Group Problem

mobius70 · Post by **mobius70** » Thu Jul 10, 2008 11:54 am

Hi

Please help me with this abstract algebra problem.
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 · Post by **lime** » Fri Jul 11, 2008 6:30 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 · Post by **diman** » Tue Jul 15, 2008 1:14 pm

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 · Post by **mathsubboy** » Sun Jul 20, 2008 10:18 pm

you are welcome!