Generalized Coxeter Groups

sage.categories.generalized_coxeter_groups.GeneralizedCoxeterGroups

The category of generalized Coxeter groups.

A generalized Coxeter group is a group with a presentation of the following form:

\[\langle s_i \mid s_i^{p_i}, s_i s_j \cdots = s_j s_i \cdots \rangle,\]

where \(p_i > 1\), \(i \in I\), and the factors in the braid relation occur \(m_{ij} = m_{ji}\) times for all \(i \neq j \in I\).

EXAMPLES:

sage: from sage.categories.generalized_coxeter_groups import GeneralizedCoxeterGroups
sage: C = GeneralizedCoxeterGroups(); C
Category of generalized coxeter groups