= Shortest conjugacy representative
A <shortest conjugacy representative> is a word having the fewest written letters among all words representing elements of a fixed <conjugacy class>. This minimum equals the least group <word length> of an element in the class; a longer spelling of that element is not itself a shortest representative. Such a word exists because lengths are nonnegative integers. It is freely and cyclically reduced: free cancellation shortens the same representative, while removing mutually inverse first and last letters shortens a conjugate. Every cyclic rotation has the same minimal length.
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