differential Galois group

Target entity: differential Galois group
Context triple: [Picard–Vessiot theory, usesConcept, differential Galois group]

• A. Picard–Vessiot theory
  Picard–Vessiot theory is a branch of differential Galois theory that studies linear differential equations via the symmetries of their solution fields, analogous to classical Galois theory for polynomial equations.
• B. Galois group
  A Galois group is the group of field automorphisms of a field extension that captures the symmetries of its algebraic equations and underpins much of modern algebra and number theory.
• C. cosmic Galois group
  The cosmic Galois group is a conjectural symmetry group acting on periods and structures arising in quantum field theory and arithmetic geometry, proposed to unify and explain deep relations between Feynman integrals, motives, and number-theoretic phenomena.
• D. Fuchsian differential equation
  A Fuchsian differential equation is a type of linear ordinary differential equation characterized by having only regular singular points, extensively studied in complex analysis and the theory of special functions.
• E. Galois theory
  Galois theory is a branch of abstract algebra that studies field extensions and polynomial equations through the structure of their associated symmetry groups.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: differential Galois group
Target entity description: A differential Galois group is the group of differential field automorphisms of a Picard–Vessiot extension that captures the algebraic symmetries of solutions to a linear differential equation.

• A. Picard–Vessiot theory
  Picard–Vessiot theory is a branch of differential Galois theory that studies linear differential equations via the symmetries of their solution fields, analogous to classical Galois theory for polynomial equations.
• B. Galois group
  A Galois group is the group of field automorphisms of a field extension that captures the symmetries of its algebraic equations and underpins much of modern algebra and number theory.
• C. cosmic Galois group
  The cosmic Galois group is a conjectural symmetry group acting on periods and structures arising in quantum field theory and arithmetic geometry, proposed to unify and explain deep relations between Feynman integrals, motives, and number-theoretic phenomena.
• D. Fuchsian differential equation
  A Fuchsian differential equation is a type of linear ordinary differential equation characterized by having only regular singular points, extensively studied in complex analysis and the theory of special functions.
• E. Galois theory
  Galois theory is a branch of abstract algebra that studies field extensions and polynomial equations through the structure of their associated symmetry groups.
• F. None of above. chosen