Maximal subgroups of SL(n, Z)

2015/11/18 by Tsachik Gelander, Gelander, Tsachik, Chen Meiri +1
Mathematics · #11F06 #20G15 #20H20 #22E40 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:11F06 #msc:20G15 #msc:20H20 #msc:22E40

paper · pdf · doi:10.48550/arxiv.1511.05767

18 pages, 0 figures

arxiv created 2016/04/17 · arxiv updated 2016/04/19

Abstract

We establish the existence of maximal subgroups of various diferent natures in SL(n,Z). In particular, we prove that there are continuously many 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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