Triplet Generator

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.