Exercise 4(30 points)
a) List all the elements of SL(2, F3) and find |SL(2, F3)|.
b) Show for any q, with q a prime number and for any n,
GL(n, Fq)/SL(n, Fq) ? Fq {0}.
c) Hence prove,
|GL(2, F3)| = 2|SL(2, F3)|.
d) Find 2 proper subgroups of SL(2, F3) which have an order at least 3.
e)
C = {[[1, 0], [0, 1]], [[2, 0], [0, 2]]}
Show that C is a normal subgroup of SL(2, F3).