Can automorphism groups ever be infinitely generated in more than a finite number of dimensions?

DOI10.1016/0001-8708(89)90051-0zbMath0684.20027OpenAlexW2001120561MaRDI QIDQ1825279

Seymour Bachmuth, Horace Y. Mochizuki

Publication date: 1989

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(89)90051-0

zbMATH Keywords

free groupfree metabelian groupsfinitely generatedinfinite generation of automorphism groupstame elements

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Automorphisms of infinite groups (20E36) Other matrix groups over rings (20H25) Automorphism groups of groups (20F28) Free nonabelian groups (20E05)

Cites Work

• The structure of the Torelli group. I: A finite set of generators for \({\mathcal I}\)
• The genus 2 Torelli group is not finitely generated
• On automorphisms of free centre-by-metabelian groups
• Some finitely presented subgroups of the automorphism group of a free group
• IA-automorphism of certain two-generator torsion-free groups
• [https://portal.mardi4nfdi.de/wiki/Publication:3658196 E 2 � SL 2 for Most Laurent Polynomial Rings]
• [https://portal.mardi4nfdi.de/wiki/Publication:3695463 Aut(F) →Aut(F/F � � ) is Surjective for Free Group F of Rank 4]
• The Nonfinite Generation of Aut(G), G Free metabelian of Rank 3
• ON THE STRUCTURE OF THE SPECIAL LINEAR GROUP OVER POLYNOMIAL RINGS
• The Automorphism Group of a Free Group Is Not a Cat(0) Group
• The free centre-by-metabelian groups
• IA automorphisms of free and free metabelian groups
• Mapping class groups and their relationship to braid groups
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