Published online by Cambridge University Press: 20 January 2009
We investigate the equivalence classes of normal subdirect products of a product of free groups Fn1 × … × Fnk under the simultaneous equivalence relations of commensurability and conjugacy under the full automorphism group. By abelianisation, the problem is reduced to one in the representation theory of quivers of free abelian groups. We show there are infinitely many such classes when k≧3, and list the finite number of classes when k = 2.
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