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: Burnside's lemma | Statement: [William Burnside, knownFor, Burnside's lemma]

Target entity: Burnside's lemma
Context triple: [William Burnside, knownFor, Burnside's lemma]

• A. Burnside's lemma chosen
  Burnside's lemma is a result in group theory and combinatorics that counts distinct configurations under symmetries by averaging the number of fixed points of group actions.
• B. Pólya enumeration theorem
  The Pólya enumeration theorem is a fundamental result in combinatorics that counts distinct configurations of objects under group actions by using cycle index polynomials and generating functions.
• C. orbit-stabilizer theorem
  The orbit-stabilizer theorem is a fundamental result in group theory that relates the size of a group acting on a set to the sizes of the orbit of an element and its stabilizer subgroup.
• D. 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.
• E. Sylow theorems
  The Sylow theorems are fundamental results in finite group theory that describe the existence, conjugacy, and number of subgroups whose orders are powers of a prime dividing the group order.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.