Alternating subgroups of Coxeter groups and their spinor extensions
  Let $G$ be a discrete Coxeter group, $G^+$ its alternating subgroup and $\tilde{G}^+$ the spinor cover of $G^+$. A presentation of the groups $G^+$ and $\tilde{G}^+$ is proved for an arbitrary Coxeter system $(G,S)$; the generators are related to edges of the Coxeter graph. Results of the Coxeter--Todd algorithm - with this presentation - for the chains of alternating groups of types A, B and D are given. 
O. V. Ogievetsky and L. Poulain d'Andecy
math.GR math-ph math.MP