Abstract
We establish the existence of maximal subgroups of various different natures in SL(n, ℤ). In particular, we prove that there are 2ϰ0 maximal subgroups, we provide a maximal subgroup whose action on the projective space has no dense orbits, and we produce a faithful primitive permutation representation of PSL(n, ℤ) which is not 2-transitive.
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