An Automorphism of A Free Metabelian Group Without Fixed Points

2003/11/26 by Martin Kassabov, Kassabov, Martin
Mathematics · #22F28 #FOS: Mathematics #Group Theory (math.GR) #Primary 20E05 #Secondary 20E36 #math.GR #msc:20E05 #msc:20E36 #msc:22F28

paper · pdf · doi:10.48550/arxiv.math/0311490

5 pages

arxiv created 2003/11/26 · arxiv updated 2009/12/01

Abstract

We construct an example of an IA-automorphism of the free metabelian group of rank n≥ 3 without nontrivial fixed points. That gives a negative answer to the question raised by Shpilrain. By a result of Bachmuth \citeBa1, such an automorphism does not exist if the rank is equal to 2.

Related

• Quotient groups of IA-automorphisms of free metabelian groups
• Chein Automorphisms of Free Metabelian Anticommutative Algebras
• Fixed points of endomorphisms of a free metabelian group
• Automorphisms of free metabelian Lie algebras, I
• Erroneous proofs of the wildness of some automorphisms of free metabelian Lie algebras