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Coxeter covers of the symmetric groups | | Louis H. Rowen
; Mina Teicher
; Uzi Vishne
; | | Date: |
11 May 2004 | | Subject: | Group Theory; Algebraic Geometry | math.GR math.AG | | Abstract: | We study Coxeter groups from which there is a natural map onto a symmetric group. Such groups have natural quotient groups related to presentations of the symmetric group on an arbitrary set $T$ of transpositions. These quotients, denoted here by C_Y(T), are a special type of the generalized Coxeter groups defined in cite{CST}, and also arise in the computation of certain invariants of surfaces. We use a surprising action of $S_n$ on the kernel of the surjection $C_Y(T)
a S_n$ to show that this kernel embeds in the direct product of $n$ copies of the free group $pi_1(T)$ (with the exception of $T$ being the full set of transpositions in $S_4$). As a result, we show that the groups $C_Y(T)$ are either virtually Abelian or contain a non-Abelian free subgroup. | | Source: | arXiv, math.GR/0405185 | | Services: | Forum | Review | PDF | Favorites | |
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