Topological generation of special linear groups

2018/01/30 by Gerhardt, Spencer
#20G15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1801.10065

Abstract

Let C₁,…,C_e be noncentral conjugacy classes of the algebraic group G=SL_n(k) defined over a sufficiently large field k, and let Ω:=C₁× … × C_e. This paper determines necessary and sufficient conditions for the existence of a tuple (x₁,…,x_e)∈Ω such that ⟨ x₁,…,x_e⟩ is Zariski dense in G. As a consequence, a new result concerning generic stabilizers in linear representations of algebraic groups is proved, and existing results on random (r,s)-generation of finite groups of Lie type are strengthened.

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