Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: O(3) | Statement: [SO(3), isNormalSubgroupOf, O(3)]

Target entity: O(3)
Context triple: [SO(3), isNormalSubgroupOf, O(3)]

• A. SU(3)
  SU(3) is the special unitary group of degree three, a Lie group fundamental to the mathematical description of the strong interaction and the classification of hadrons in particle physics.
• B. rotation group SO(3)
  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.
• C. special orthogonal group SO(n)
  The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
• D. O.
  O. is the middle initial of Mark O. Hatfield, the long-serving U.S. Senator and former Governor of Oregon.
• E. orthogonal group O(n) chosen
  The orthogonal group O(n) is the group of all n×n real matrices that preserve the standard Euclidean inner product, representing rotations and reflections in n-dimensional space.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: isNormalSubgroupOf
Context triple: [SO(3), isNormalSubgroupOf, O(3)]

• A. hasNormalSubgroup chosen
  Indicates that one group is a normal subgroup of another group, meaning it is invariant under conjugation by elements of the larger group.
• B. isMaximalSubgroupOf
  Indicates that one group is a proper subgroup of another that is not contained in any larger proper subgroup of that group.
• C. isClosedSubgroupOf
  Indicates that one group is a subgroup of another and is closed in the topological sense within that larger group.
• D. isBosonicSubgroupOf
  Indicates that one group consists only of bosonic elements and is contained as a subgroup within another group.
• E. isSemidirectProductOf
  Indicates that a group is constructed as a semidirect product of two subgroups, where one subgroup acts on the other via automorphisms in a way that generalizes the direct product.
• F. None of above.