Coxeter covers of the classical Coxeter groups
M. Amram, R. Shwartz, M. Teicher

TL;DR
This paper characterizes certain generalized Coxeter groups as semidirect products involving Abelian groups and classical Coxeter groups, extending previous results to a broader class of groups.
Contribution
It provides a new isomorphism classification for quotients of generalized Coxeter groups onto classical Coxeter groups, including cases with loops in the associated graphs.
Findings
C_Y(T) is isomorphic to A_{t,n} semidirect B_n or D_n
The structure depends on whether the graph T contains loops
The number of cycles in T determines t
Abstract
Let be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either or . Let be a natural quotient of , and if is simply-laced (which means all the relations between the generators has order 2 or 3), is a generalized Coxeter group, too . Let be a group which contains Abelian groups generated by elements. The main result in this paper is that is isomorphic to or , depends on whether the signed graph contains loops or not, or in other words C(T) is simply-laced or not, and is the number of the cycles in . This result extends the results of Rowen, Teicher and Vishne to generalized Coxeter groups which have a natural map onto one of the classical Coxeter groups.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · semigroups and automata theory
