Artin group

In mathematics, an Artin group is a group with a presentation of the form

With

For it means the alternating product of the length of and starting with. So, for example,

Or

Means that there are no relations between and.

Artin groups are named after the mathematician Emil Artin.

Special cases

Braid groups

Braid groups is obtained as a special case with

And

Right-angled Artin groups

Right-angled Artin groups are Artin groups with

For everyone. They play an important role in the 3-dimensional topology.

• Group (mathematics)
• Group Theory