The uses of 2 by 2 matrices in combinatorial group theory. A survey

DOI10.1007/BF03322976zbMath0468.20031MaRDI QIDQ1156235

Wilhelm Magnus

Publication date: 1981

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

zbMATH Keywords

Bibliographyfundamental groupsFuchsian groupsfinitely presented groupstrace formulasone relator groupsknot groupslocally free groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Other groups related to topology or analysis (20F38) Automorphism groups of groups (20F28) Other matrix groups over fields (20H20)

Related Items

Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Topological components of spaces of representations, Faithful actions of automorphism groups of free groups on algebraic varieties, Valuations on the character variety: Newton polytopes and residual Poisson bracket, Spectrum Maximizing Products Are Not Generically Unique, Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics., Automorphisms of groups, Some decision problems on integer matrices, A faithful polynomial representation of Out F₃, Algebraic geometric invariants for a class of one-relator groups, The conjugacy problem of the modular group and the class number of real quadratic number fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finite integrity bases for five or fewer symmetric 3 \(\times\) 3 matrices
• Rings of Fricke characters and automorphism groups of free groups
• The invariant theory of \(n\times n\) matrices
• Characters of \(F_2\) represented in \(Sp(4,R)\)
• Trace identities and polynomial identities of \(n\times n\) matrices
• Von Untergruppen der Triangel-Gruppen
• Über das Geschlecht von Knoten
• Free subgroups of groups with a single defining relation
• Fuchsian groups contained in \(SL_ 2(\mathbb{Q})\)
• Two generator Fuchsian groups of genus one
• Free subgroups in linear groups
• Diskrete Untergruppen von \(SL_2 (R)\).
• Fuchssche Gruppen, die freies Produkt zweier zyklischer Gruppen sind, und die Gleichung \(x^2+y^2+z^2=xyz\).
• KNOTS WITH THE PARABOLIC PROPERTY P
• Induced Automorphisms on Fricke Characters of Free Groups
• A quadratic parabolic group
• Parabolic Representations of Knot Groups, II
• Discrete parabolic representations of link groups
• On Triple Planes (III)
• Hecke invariants of knot groups
• Characters of free groups represented in the two‐dimensional special linear group
• On knot groups
• Groups with the Same lower Central Sequence as a Relatively Free Group. II. Properties
• Torsion-Free Subgroups of Triangle Groups
• Homomorphisms of Knot Groups on Finite Groups
• Parabolic Representations of Knot Groups, I
• On Special Linear Characters of Free Groups of Rank n ≧4
• On Representations of the Group of Listing's Knot by Subgroups of SL(2, C )
• A Finitely Generated Infinite Simple Group