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Conjugacy problems in GL(n,Z)

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GRAW02 - Computational and algorithmic methods

The talk describes a practical algorithm to solve the conjugacy and the centralizer problems in GL(n,Z) in full generality; that is, given two matrices A and B in GL(n,Q) these algorithms allow to check if A and B are conjugate in GL(n,Z) and, if so, then to determine a conjugating element, and they allow to compute generators for the centralizer of A in GL(n,Z).  The talk also discusses possible extensions of this algorithm to finitely generated abelian or nilpotent subgroups of GL(n,Z). The latter are open problems in computational group theory and they have interesting applications.

This talk is part of the Isaac Newton Institute Seminar Series series.

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