Structures Of Some Kinds Of Primitive Words

D.Borwein proved that if u is a non-empty word and a is a word with length of 1 satisfying u isn’t a powers of a, then at least one of u and ua is a primitive word. In 2002, Gheorghe Paun and Nicolae Son proved that if u is a non-empty word and a, b are two distinct words with each length of I, then at least one of ua and ub is primitive word. In this paper, we have proved two results of primitive properties as follows:(1) if u is a non-empty word and p is a word with length not longer than three satisfying up≠pu, then at least one of u and up is a primitive word; (2) if u is a non-empty word and p and q are two distinct words with length not longer than two satisfying pq≠qp, then at least one of up and uq is a primitive word.