Normalizers of compact subgroups, the existence of commuting automorphisms, and applications to operator semistable measures.

Hazod, W.; Hofmann, K.H.; Scheffler, H.-P.; Wüstner, M.; Zeuner, H.

Displaying similar documents to “Normalizers of compact subgroups, the existence of commuting automorphisms, and applications to operator semistable measures.”

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-- We exhibit normal subgroups of a free nilpotent group F of rank two and class three, which have isomorphic finite quotients but are not conjugate under any automorphism of F.

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2000 Mathematics Subject Classification: 17B01, 17B30, 17B40. Let Lm,c be the free m-generated metabelian nilpotent of class c Lie algebra over a field of characteristic 0. An automorphism φ of Lm,c is called normal if φ(I) = I for every ideal I of the algebra Lm,c. Such automorphisms form a normal subgroup N(Lm,c) of Aut (Lm,c) containing the group of inner automorphisms. We describe the group of normal automorphisms of Lm,c and the quotient group of Aut (Lm,c) modulo N(Lm,c). ...