"Dyer groups are CAT(0)"
Soergel, MireilleWhen studying the solution to the word problem in Coxeter groups and in graph products of cyclic groups, one might notice that they are the same. Tits and Green both show that a word is reduced if and only if it cannot be reduced by a series of elementary M-transformations. Matthew Dyer described a class of groups, which we call Dyer groups, which are characterized by such a solution to the word problem. This class includes, but is not limited to, Coxeter groups, right angled Artin groups, and graph products of finite cyclic groups. We will introduce Dyer groups by giving their standard presentation and give some of their properties.