Supports of derivations, free factorizations, and ranks of fixed subgroups in free groups

DOI10.1090/S0002-9947-99-02087-5zbMath0926.20016OpenAlexW1552373856WikidataQ114093889 ScholiaQ114093889MaRDI QIDQ4226686

George M. Bergman

Publication date: 27 January 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02087-5

zbMATH Keywords

endomorphismsderivationsfree groupsfixed subgroups

Mathematics Subject Classification ID

Automorphisms of infinite groups (20E36) Fundamental group, presentations, free differential calculus (57M05) Free nonabelian groups (20E05)

Related Items (19)

Fixed Subgroups are Compressed in Free Groups ⋮ Intersections of automorphism fixed subgroups in the free group of rank three. ⋮ POLYNOMIAL ENDOMORPHISMS PRESERVING OUTER RANK IN TWO VARIABLES ⋮ Algebraically and verbally closed subgroups and retracts of finitely generated nilpotent groups ⋮ On free decompositions of verbally closed subgroups in free products of finite groups ⋮ Fixed subgroups are compressed in surface groups ⋮ Primitive and almost primitive elements of Schreier varieties ⋮ The group fixed by a family of endomorphisms of a surface group ⋮ Fixed subgroups in direct products of surface groups of Euclidean type ⋮ Examples of retracts in free groups that are not the fixed subgroup of any automorphism. ⋮ Verbally closed subgroups of free solvable groups ⋮ Fixed subgroups of endomorphisms of free products. ⋮ Products of test elements of free factors of a free group ⋮ Computing fixed closures in free groups. ⋮ Aspects of free groups. ⋮ Primitive, almost primitive, test, and \(\Delta\)-primitive elements of free algebras with the Nielsen-Schreier property ⋮ On equalizers of sections. ⋮ On automorphism-fixed subgroups of a free group ⋮ Verbally and existentially closed subgroups of free nilpotent groups.

Cites Work

• Intersections of finitely generated subgroups of free groups and resolutions of graphs
• What does a basis of F(a,b) look like?
• On equalizers of sections.
• Embedding rings in completed graded rings. III: Algebras over general k
• Fixed Subgroups of Homomorphisms of Free Groups
• Endomorphisms of free groups and their fixed points
• All automorphisms of free groups with maximal rank fixed subgroups
• The Group Fixed by a Family of Injective Endomorphisms of a Free Group
• Test Words for Automorphisms of Free Groups
• On the Number of Generators of a Free Product
• Some Properties of Free Groups
• Groups of cohomological dimension one
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