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- W2950641010 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 $C_Y(T) ra S_n$ 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." @default.
- W2950641010 created "2019-06-27" @default.
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- W2950641010 date "2004-05-11" @default.
- W2950641010 modified "2023-09-27" @default.
- W2950641010 title "Coxeter covers of the symmetric groups" @default.
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