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  1. Normal subgroups of nonstandard symmetric and alternating groups.John Allsup & Richard Kaye - 2007 - Archive for Mathematical Logic 46 (2):107-121.
    Let ${\mathfrak{M}}$ be a nonstandard model of Peano Arithmetic with domain M and let ${n \in M}$ be nonstandard. We study the symmetric and alternating groups S n and A n of permutations of the set ${\{0,1,\ldots,n-1\}}$ internal to ${\mathfrak{M}}$ , and classify all their normal subgroups, identifying many externally defined such normal subgroups in the process. We provide evidence that A n and S n are not split extensions by these normal subgroups, by showing that any such complement if (...)
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