Recognizing automorphisms of the free groups

DOI10.1007/BF01196426zbMath0802.20024OpenAlexW2000886002MaRDI QIDQ1327118

Vladimir Shpilrain

Publication date: 14 December 1994

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01196426

zbMATH Keywords

endomorphismsgeneratorsautomorphismsgroup ringsfree groupsfully invariant subgroupsinverse function theoremcommutator testfree derivatives

Mathematics Subject Classification ID

Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Generators, relations, and presentations of groups (20F05) Automorphisms of infinite groups (20E36) Free nonabelian groups (20E05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Commutator calculus (20F12)

Related Items (26)

Test elements of direct sums and free products of free Lie algebras ⋮ PRIMITIVITY PRESERVING ENDOMORPHISMS OF FREE GROUPS ⋮ Test elements in pro-\(p\) groups with applications in discrete groups ⋮ Endomorphisms preserving an orbit in a relatively free nilpotent group ⋮ Generic elements of free groups ⋮ Some combinatorial questions about polynomial mappings ⋮ Test elements for endomorphisms of free groups and algebras ⋮ Primitive and almost primitive elements of Schreier varieties ⋮ Automorphic and endomorphic reducibility and primitive endomorphisms of free metabelian groups ⋮ Test elements and retracts of free Lie algebras^‡ ⋮ Products of test elements of free factors of a free group ⋮ Automorphic orbit problem for polynomial algebras ⋮ Test elements, retracts and automorphic orbits. ⋮ Orbits in free algebras of rank two ⋮ AUTOMORPHIC ORBITS IN FREE GROUPS: WORDS VERSUS SUBGROUPS ⋮ Generic, almost primitive and test elements of free Lie algebras ⋮ Automorphic orbits in free non-associative algebras ⋮ RECOGNIZING AUTOMORPHISMS OF THE FREE COLOR LIE SUPERALGEBRAS ⋮ Primitive elements and automorphisms of free algebras of Schreier varieties ⋮ Test Ranks of Free Nilpotent Groups ⋮ Test polynomials for automorphisms of polynomial and free associative algebras ⋮ On certain elements of free groups ⋮ Primitive, almost primitive, test, and \(\Delta\)-primitive elements of free algebras with the Nielsen-Schreier property ⋮ Orbits and Test Elements in Free Leibniz Algebras of Rank Two ⋮ Equations in acylindrically hyperbolic groups and verbal closedness ⋮ Endomorphisms of free groups that preserve automorphic orbits

Cites Work

• Unnamed Item
• The Mal'tsev-Nielsen equation in a free metabelian group of rank two
• Nullhomologous words in free groups which are not nullhomologous in any proper subgroup
• Generators of the group \(F/[N,N\)]
• Free differential calculus. I: Derivation in the free group ring. II: The isomerphism problem of groups. III: Subgroups
• Über Automorphismen ebener diskontinuierlicher Gruppen
• Free Group Rings
• Nielsen's commutator test for two-generator groups
• An Inverse Function Theorem for Free Groups
• Alternierende Produkte in freien Gruppen
• Alternierende Produkte in freien Gruppen

This page was built for publication: Recognizing automorphisms of the free groups