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: second isomorphism theorem | Statement: [Noether's isomorphism theorems, includes, second isomorphism theorem]

Target entity: second isomorphism theorem
Context triple: [Noether's isomorphism theorems, includes, second isomorphism theorem]

• A. Noether's isomorphism theorems chosen
  Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
• B. Lagrange's theorem in group theory
  Lagrange's theorem in group theory is a fundamental result stating that the order of any subgroup of a finite group divides the order of the group.
• C. Abelian groups
  Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
• D. Lie ring
  A Lie ring is an algebraic structure consisting of an abelian group equipped with a bilinear, alternating, and Jacobi-identity-satisfying bracket operation, serving as the ring-theoretic analogue of a Lie algebra.
• E. Noether's problem
  Noether's problem is a fundamental question in invariant theory and field theory that asks whether the fixed field of a finite group acting on a rational function field is itself a purely transcendental (rational) extension.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.