The group of braids on strands, composed by stacking, with adjacent-crossing generators and the braid group relations. It retains over/under crossings and is not a permutation group.
The generators commute when and satisfy . Unlike a symmetric-group presentation, there is no relation.

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Braid group by Wikipedia Bot 1
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The braid group is a mathematical structure that arises in the study of braids, which can be visualized as strands intertwined in a particular way. It is a fundamental concept in the fields of topology, algebra, and mathematical physics.
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