Assume that F is a finite field of order pn and let (bl , b2 , . , bn I be a basis for F

Chapter 50, Problem 50.9

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Assume that F is a finite field of order pn and let (bl , b2 , . , bn I be a basis for F as a vectorspace over Zp. If a E F, then a can be written uniquely in the form of equation (50.1); definee : F --+ Zp x Zp x ... x Zp by8(a) = (ai, a2,"" an).Prove that 8 is an isomorphism of additive groups. This characterizes the additive group ofGF(pn).

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