Group Theory, Algebra, and Number Theory

Colloquium in Memory of Hans Zassenhaus held in Saarbrücken, Germany, June 4-5, 1993

Horst G. Zimmer

• Publisher: De Gruyter
• Year: 2011
• Print ISBN:
  9783110153477
• eBook ISBN:
  9783110811957
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

No detailed description available for "Group Theory, Algebra, and Number Theory".

Table of contents

• Introductory address
• After-dinner speech
• On the solvability of the kernel of any orthogonal decomposition
• 1. Introduction
• 2. Lie algebras of types Bn,Cn, and Dn
• 3. Exceptional Lie algebras
• 4. Lie algebras of type An
• References
• The beginnings of modular Lie algebra theory
• 1. Introduction
• 2. Zassenhaus algebra
• 3. Lie algebras of Cartan type
• 4. Derivations
• 5. Sandwiches, filiations, ‘classicality’ criterion
• 6. Linear representations and Cartan prolongations
• 7. Lie algebras over fields of small characteristic
• 7.1. Characteristic p = 5
• 7.2. Characteristic p = 3
• 7.3. Characteristic p = 2
• 8. Miscellaneous
• References
• Computing invariants of algebraic number fields
• 1. Introduction
• 2. Galois groups
• 2.1. (B) Approximation of Γ from below
• 2.2. (A) Approximation of Γ from above and verification
• 3. Integral basis
• 3.1. Round 2-method
• 3.2. Round 4-method
• 4. Unit group and class group
• 4.1. Method I (assuming GRH)
• 4.2. Method II (unconditional)
• 5. Examples and applications
• References
• Kristallographische Gruppen
• 1. Einleitung
• 2. Die Periode bis 1950 aus heutiger Sicht
• 3. Die vierdimensionalen Raumgruppen
• 4. Spätere Entwicklungen
• 5. Beispiele von Bravaismannigfaltigkeiten
• Literatur
• Endliche Fastkörper und Zassenhausgruppen
• 1. Einleitung
• 2. Zur Kommutativität endlicher Divisionsringe
• 3. Gruppen mit Partition
• 4. Mehr über fixpunktfreie Operation
• 5. Gruppen mit pq-Bedingung
• 6. Ausnahmecharaktere und der SL2(5)-Satz von Zassenhaus
• 7. Das Isomorphieproblem
• 8. Die 2-dimensionalen linearen Gruppen und der SL2(5)-Satz von Dickson
• 9. Vollständige Fastkörper
• 10. Zassenhausgruppen
• Literatur
• On the arithmetic of commutative group rings
• 1. Introduction
• 2. Constructible units
• 3. Cyclic p-groups
• 4. Functors on cyclotomic algebras
• 4.1. Admissible functors
• 4.2. Cyclogenic functors
• 5. Local units and logarithms
• 5.1. Polarized bases
• 5.2. ogarithms and applications
• 6. Regular primes
• 6.1. Arithmetical background
• 6.2. Abelian p-groups
• 7. Irregular primes
• 7.1. A converse
• 7.2. Non-constructible units
• 8. Local units and global ideal classes
• 8.1. Normal bases for local units
• 8.2. Comparison with global units
• 8.3. Kernel groups
• 9. Cyclic groups of composite order
• 9.1. An exact sequence
• 9.2. Even order
• 9.3. Odd order
• References