Combinatorial Group Theory

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2 domain-specific abstractions whose origin domain is Combinatorial Group Theory.

• Conjugacy problem — Decide whether two words in a finitely generated or finitely presented group represent conjugate elements, with solvability depending on the group class and presentation rather than group axioms alone.
• Word problem for groups — Decide whether two finite words in a group's generators represent the same element, equivalently whether their quotient word represents the identity; finitely presented groups can make this problem undecidable.