Cyclically reduced word

In mathematics, cyclically reduced word is a concept of combinatorial group theory.
Let F(X) be a free group. Then a word w in F(X) is said to be cyclically reduced if and only if every cyclic permutation of the word is reduced.
Properties
 Every cyclic shift and the inverse of a cyclically reduced word are cyclically reduced again.
 Every word is conjugate to a cyclically reduced word. The cyclically reduced words are minimallength representatives of the conjugacy classes in the free group. This representative is not uniquely determined, but it is unique up to cyclic shifts (since every cyclic shift is a conjugate element).
References
 Solitar, Donald; Magnus, Wilhelm; Karrass, Abraham (1976), Combinatorial group theory: presentations of groups in terms of generators and relations, New York: Dover, pp. 33,188,212, ISBN 0486632814
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