Nielsen's commutator test for two-generator groups

DOI10.1017/S0305004100071590zbMath0793.20023OpenAlexW1979356322MaRDI QIDQ4277217

Vladimir Shpilrain, Narain Gupta

Publication date: 18 August 1994

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100071590

zbMATH Keywords

endomorphismcommutatorlower central seriesfree generatorsfree polynilpotent groupfree group ringsfree group of rank twoexistence of non-tame automorphismstwo- generator groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Automorphisms of infinite groups (20E36) Free nonabelian groups (20E05) Quasivarieties and varieties of groups (20E10) Derived series, central series, and generalizations for groups (20F14)

Related Items

Recognizing automorphisms of the free groups ⋮ Generic elements of free groups ⋮ Test elements for endomorphisms of free groups and algebras ⋮ Free nilpotent groups of rank 2 ⋮ Primitive, almost primitive, test, and \(\Delta\)-primitive elements of free algebras with the Nielsen-Schreier property

Cites Work

• The Mal'tsev-Nielsen equation in a free metabelian group of rank two
• IA-automorphism of certain two-generator torsion-free groups
• Applications of a New K-Theoretic Theorem to Soluble Group Rings
• Non-tame automorphisms of free nilpotent groups
• Free Group Rings
• Tame range of automorphism groups of free polynilpotent groups
• AUTOMORPHISMS OF F/R′ GROUPS
• Non-tame automorphisms of free nilpotent groups of rank 2
• Induced Automorphisms of Free Groups and Free Metabelian Groups
• On the Automorphisms of Free Groups and Free Nilpotent Groups
• Varieties of groups
• A Note on Zero Divisors in Group-Rings
• Commutator Subgroups of Free Groups

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