Finitely presented and residually finite implies solvable word problem
This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., finitely presented residually finite group) must also satisfy the second group property (i.e., group with solvable word problem)
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- Finitely presented implies all homomorphisms to any finite group can be listed in finite time
- Residually finite and all homomorphisms to any finite group can be listed in finite time implies solvable word problem
The proof follows directly by combining Facts (1) and (2).