Artin group

In mathematics, an Artin group (or generalized braid group) is a group with a presentation of the form

where

For ${\displaystyle m<\infty }$, ${\displaystyle \langle x_{i},x_{j}\rangle ^{m}}$ denotes an alternating product of ${\displaystyle x_{i}}$ and ${\displaystyle x_{j}}$ of length ${\displaystyle m}$, beginning with ${\displaystyle x_{i}}$. For example,

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