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answered May 25, 2010 at 22:11

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No. This is explicitly stated in the paragraph above Theorem 1 of:

Turner, Edward C, Test words for automorphisms of free groups. Bull. London Math. Soc. 28 (1996), no. 3, 255--263.

The author refers to Proposition 1.

answered May 25, 2010 at 22:11

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