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The Triplet Generator generates a list of basic triplets with two concepts and a true relation between them, given a LIST OF CONCEPTS unders a specific FIELD OF STUDY. No repeats or incorrect triplets 🔍 Find my "FIELD OF KNOWLEDGE LISTER" and "CONCEPT LISTER" on Prompt Base to get to this point much quicker. 🤙👊🏻✅
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Over 1 month ago
Prompt Details
Model
Chat - GPT-3.5 (gpt-3.5-turbo)
Token size
173 ($0.00030 / call)
Example input
[Field of study]: Group theory
[List of concepts]: Group
Subgroup
Normal Subgroup
Quotient Group
Homomorphism
Isomorphism
Automorphism
Group Action
Orbit
Stabilizer
Permutation Group
Symmetric Group
Alternating Group
Sylow Subgroup
Solvable Group
Simple Group
Composition Series
Direct Product
Direct Sum
Finitely Generated Abelian Group
Free Group
Presentation of a Group
Commutator
Center of a Group
Conjugacy Class
Class Equation
Burnside's Lemma
Cayley's Theorem
Schur's Lemma
Poincaré Conjecture
Example output
My task is to generate an extensive and comprehensive list of basic triplets which contain two concepts and a true relation between them from the provided list of concepts.
Here is the list of basic triplets combining the provided concepts:
is a - subgroup - group
is a - normal subgroup - group
is a - quotient group - group
is a - homomorphism - group
is an - isomorphism - group
is an - automorphism - group
acts on - group - set
is an - orbit - group element
is a - stabilizer - group element
is a - permutation group - set
is a - symmetric group - set
is an - alternating group - set
is a - Sylow subgroup - group
is a - solvable group - group
is a - simple group - group
has a - composition series - group
is a - direct product - group
is a - direct sum - group
is a - finitely generated abelian group - group
is a - free group - set
has a - presentation - group
has a - commutator - group
has a - center - group
has a - conjugacy class - group element
has a - class equation - group
applies - Burnside's Lemma - group and set
satisfies - Cayley's Theorem - group
applies - Schur's Lemma - group representation
implies - Poincaré Conjecture - topology
In conclusion, these basic triplets provide a fundamental understanding of the various concepts and relationships in group theory. They serve as a useful tool for knowledge representation and help in the formulation of further concepts and theories in the field.