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19.60 (2018)

Open

Let $R$ be a principal ideal domain, let $d$ be a positive integer, and let $X_1, \dots, X_m$ be members of $\text{SL}(d, R)$ (or of $\text{GL}(d, R)$). Is it decidable whether or not these $m$ matrices freely generate a free group? If it is, design an effective algorithm for computing the answer.

Contributor: P. M. Neumann

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