Automorphism groups of nilpotent groups and spaces
In this article the following main results are obtained. Theorem. There exist finitely generated, torsion-free nilpotent groups \(G_1\), \(G_2\) in the same localization genus whose automorphism groups \(\Aut(G_1)\), \(\Aut(G_2)\) are not isomorphic. Corollary. There exist finite, aspherical CW-complexes (indeed, closed smooth manifolds) \(Y_1\), \(Y_2\) in the same localization genus whose automorphism groups \(\Aut(Y_1)\), \(\Aut(Y_2)\) are not isomorphic. More precisely, \(Y_1\), \(Y_2\) are closed, smooth manifolds which are Eilenberg-MacLane spaces \(K(G_1,1)\), \(K(G_2,1)\), where \(G_1\), \(G_2\) are groups of the kind occuring in the theorem.
scientific article; zbMATH DE number 1501627