As a group under addition, <i>GF</i>(<i>p<sup>n</sup></i>)
is isomorphic to <br><i> Z<sub>p</sub> &#8853 &#8230 
&#8853 Z<sub>p</sub></I> 
 (with <i>n</i>  factors). <BR> 

As a group under multiplication, the set of nonzero elements of 
<i>GF</i>(<i>p<sup>n</sup></i>)
is isomorphic to <i> Z<sub>p<sup>n</sup> - 1</i> (and is, therefore, cyclic).