Sentence:  Likewise, \alpha^{2^n}=\alpha, etc., namely, the elements are all expressed as powers of \alpha and because \alpha^{2^n-1}=1, \alpha is termed a <WSD>primitive element</WSD> of \mathrm{GF}(2^n).... / Furthermore, if the irreducible polynomial has a <WSD>primitive element</WSD> \alpha (where \alpha^{2^n-1} = 1) that is a root, then the polynomial is termed a primitive polynomial and corresponds to the polynomial for a maximal length feedback shift register. 
Meaning of the word marked with <WSD> tags:  An element that generates the multiplicative group of a given Galois field (finite field).