Displaying similar documents to “Cohomological dimension and symmetric automorphisms of a free group.”

The Automorphism Group of the Free Algebra of Rank Two

Cohn, P. (2002)

Serdica Mathematical Journal

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The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate...

Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

Fιndιk, Şehmus (2010)

Serdica Mathematical Journal

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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). ...