rotation group SO(3)

Target entity: rotation group SO(3)
Context triple: [Lorentz group, hasSubgroup, rotation group SO(3)]

• A. Lorentz group
  The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
• B. Euclidean group
  The Euclidean group is the group of all distance-preserving transformations of Euclidean space, consisting of rotations, reflections, and translations.
• C. Sophus
  Sophus was the given name of the Norwegian mathematician Sophus Lie, a pioneer in the theory of continuous transformation groups now known as Lie groups.
• D. Galilean group
  The Galilean group is the mathematical group of spacetime transformations—comprising translations, rotations, and Galilean boosts—that characterize the symmetries of classical Newtonian mechanics.
• E. Lie group
  A Lie group is a mathematical structure that is both a smooth manifold and a group, where the group operations are differentiable and used to study continuous symmetries.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: rotation group SO(3)
Target entity description: The rotation group SO(3) is the group of all rotations in three-dimensional space, represented by 3×3 orthogonal matrices with determinant 1, and plays a central role in classical mechanics, quantum mechanics, and geometry.

• A. Lorentz group
  The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
• B. Euclidean group
  The Euclidean group is the group of all distance-preserving transformations of Euclidean space, consisting of rotations, reflections, and translations.
• C. Sophus
  Sophus was the given name of the Norwegian mathematician Sophus Lie, a pioneer in the theory of continuous transformation groups now known as Lie groups.
• D. Galilean group
  The Galilean group is the mathematical group of spacetime transformations—comprising translations, rotations, and Galilean boosts—that characterize the symmetries of classical Newtonian mechanics.
• E. Lie group
  A Lie group is a mathematical structure that is both a smooth manifold and a group, where the group operations are differentiable and used to study continuous symmetries.
• F. None of above. chosen