A matrix criterion makes centralizers in GL(n, Z) polycyclic, yielding an effective Tits alternative and decidable conjugacy in integral symplectic and similar groups.
Arithmetic subgroups of algebraic groups.Annals of Mathematics, 75(3):485–535
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A criterion for Tits alternative on the centralizer of a matrix
A matrix criterion makes centralizers in GL(n, Z) polycyclic, yielding an effective Tits alternative and decidable conjugacy in integral symplectic and similar groups.