Book contents
- Frontmatter
- Contents of Volume 1
- Contents of Volume 2
- Algebraic Geometry: A Celebration of Emma Previato’s 65th Birthday
- 1 Arithmetic Analogues of Hamiltonian Systems
- 2 Algebraic Spectral Curves over Q and their Tau-Functions
- 3 Frobenius Split Anticanonical Divisors
- 4 Halves of Points of an Odd Degree Hyperelliptic Curve in its Jacobian
- 5 Normal Forms for Kummer Surfaces
- 6 σ-Functions: Old and New Results
- 7 Bergman Tau-Function: From Einstein Equations and Dubrovin-Frobenius Manifolds to Geometry of Moduli Spaces
- 8 The Rigid Body Dynamics in an Ideal Fluid: Clebsch Top and Kummer Surfaces
- 9 An Extension of Delsarte, Goethals and Mac Williams Theorem on Minimal Weight Codewords to a Class of Reed-Muller Type Codes
- 10 A Primer on Lax Pairs
- 11 Lattice-Theoretic Characterizations of Classes of Groups
- 12 Jacobi Inversion Formulae for a Curve in Weierstrass Normal Form
- 13 Spectral Construction of Non-Holomorphic Eisenstein-Type Series and their Kronecker Limit Formula
- 14 Some Topological Applications of Theta Functions
- 15 Multiple Dedekind Zeta Values are Periods of Mixed Tate Motives
- 16 Noncommutative Cross-Ratio and Schwarz Derivative
11 - Lattice-Theoretic Characterizations of Classes of Groups
Published online by Cambridge University Press: 19 March 2020
Book contents
- Frontmatter
- Contents of Volume 1
- Contents of Volume 2
- Algebraic Geometry: A Celebration of Emma Previato’s 65th Birthday
- 1 Arithmetic Analogues of Hamiltonian Systems
- 2 Algebraic Spectral Curves over Q and their Tau-Functions
- 3 Frobenius Split Anticanonical Divisors
- 4 Halves of Points of an Odd Degree Hyperelliptic Curve in its Jacobian
- 5 Normal Forms for Kummer Surfaces
- 6 σ-Functions: Old and New Results
- 7 Bergman Tau-Function: From Einstein Equations and Dubrovin-Frobenius Manifolds to Geometry of Moduli Spaces
- 8 The Rigid Body Dynamics in an Ideal Fluid: Clebsch Top and Kummer Surfaces
- 9 An Extension of Delsarte, Goethals and Mac Williams Theorem on Minimal Weight Codewords to a Class of Reed-Muller Type Codes
- 10 A Primer on Lax Pairs
- 11 Lattice-Theoretic Characterizations of Classes of Groups
- 12 Jacobi Inversion Formulae for a Curve in Weierstrass Normal Form
- 13 Spectral Construction of Non-Holomorphic Eisenstein-Type Series and their Kronecker Limit Formula
- 14 Some Topological Applications of Theta Functions
- 15 Multiple Dedekind Zeta Values are Periods of Mixed Tate Motives
- 16 Noncommutative Cross-Ratio and Schwarz Derivative
Summary
One of the most interesting problems in the field Subgroup Lattices of Groups is to find lattice-theoretic characterizations of interesting classes of groups. After explaining this problem by looking at the classical characterizations of cyclic and of finite soluble groups, we first present lattice-theoretic characterizations of some classes of infinite soluble groups. Then for a finite group G we try to determine in its subgroup lattice L(G) the Fitting length of G and properties defined by arithmetical conditions. For this we use some new ideas to determine minimal normal subgroups and the orders of minimal subgroups in L(G).
- Type
- Chapter
- Information
- Integrable Systems and Algebraic Geometry , pp. 367 - 382Publisher: Cambridge University PressPrint publication year: 2020