We derive presentations of the interval groups related to all quasi-Coxeter elements in Coxeter group type D n . Type is only infinite family finite that admits proper elements. The we obtain are over a set generators bijection with what call Carter generating set, and relations those defined by diagram together twisted cycle or commutator relator, depending on whether element not. proof based ...

Let $p$ be a prime. We produce two new families of pro-$p$ groups which are not realizable as absolute Galois fields. To prove this we use the 1-smoothness property groups. Moreover, show in these one has one-relator may ruled out employing quadraticity cohomology (a consequence Rost-Voevodsky Theorem), or vanishing Massey products cohomology.