Zariski density and computing with S-integral groups

2023/03/10 by Detinko, A. S., Flannery, D. L., Hulpke, A.
#20-04 #20G15 #20H25 #68W30 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2303.06236

Abstract

We generalize our methodology for computing with Zariski dense subgroups of SL(n, ℤ) and Sp(n, ℤ), to accommodate input dense subgroups H of SL(n, ℚ) and Sp(n, ℚ). A key task, backgrounded by the Strong Approximation theorem, is computing a minimal congruence overgroup of H. Once we have this overgroup, we may describe all congruence quotients of H. The case n=2 receives particular attention.

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