The braid group B-n, endowed with Artin's presentation, admits an antiautomorphism B-n -> B-n, such that v -> (v) over bar is defined by reading braids in reverse order (from right to left instead of left to right). We prove that the map B-n -> B-n, v -> v (v) over bar is injective. We also give some consequences arising due to this injectivity.
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