Discrete subgroups of Lie groups

introduction

• More than three decades ago, in a remarkable paper [MS81], Margulis and Soifer proved existence of maximal subgroups of infinite index in SL(n,Z), answering a question of Platonov. Moreover, they proved that there are uncountably many such subgroups. Since then, it is expected that there should be examples of various different nature. However, as the proof is non-constructive and relies on the axiom of choice, it is highly non-trivial to put the hand on specific properties of the resulting groups. Our purpose here is to show that indeed, maximal subgroups of different nature do exist.

articles

• Gelander, Tsachik, and Chen Meiri. “Maximal Subgroups of SL(n, Z).” arXiv:1511.05767 [math], November 18, 2015. http://arxiv.org/abs/1511.05767.