Cyclically reduced word
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- 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 minimal-length 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).
- 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 0-486-63281-4
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