Artin–Tits group

<p>In the <a href="/facts/Mathematics/pxTouaz4">mathematical</a> area of <a href="/facts/Group_theory/NfowcI5H">group theory</a>, Artin groups, also known as Artin–Tits groups or generalized braid groups, are a family of infinite discrete <a href="/facts/Group_(mathematics)/IQTYqINt">groups</a> defined by simple <a href="/facts/Presentation_of_a_group/f9emPUoI">presentations</a>. They are closely related with <a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter groups</a>. Examples are <a href="/facts/Free_group/zPo2NIGb">free groups</a>, <a href="/facts/Free_abelian_group/oaSRGmpY">free abelian groups</a>, <a href="/facts/Braid_group/rn5323Kx">braid groups</a>, and right-angled Artin–Tits groups, among others.
</p><p>The groups are named after <a href="/facts/Emil_Artin/rI3vIFo2">Emil Artin</a>, due to his early work on braid groups in the 1920s to 1940s, and <a href="/facts/Jacques_Tits/QyJlDmlE">Jacques Tits</a> who developed the theory of a more general class of groups in the 1960s.
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Artin–Tits group open-in-new

Artin–Tits group