Answer to Question #18555 in Abstract Algebra for Mohammad

Question

Let k be the algebraic closure of Fp and K = k(t), where t is an indeterminate. Let G be an elementary p-group of order p2 generated by a, b. Show that
a → A =
1 1
0 1

b→ B =
1 t
0 1
defines a representation of G over K which is not equivalent to any representation of G over k.