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)
View all group property implications | View all group property non-implications
Get more facts about finitely presented residually finite group|Get more facts about group with solvable word problem

Statement

Any finitely presented residually finite group (i.e., a group that is both a finitely presented group and a residually finite group) is a group with solvable word problem.

Related facts

Similar facts

• Finitely presented and conjugacy-separable implies solvable conjugacy problem

Facts used

1. Finitely presented implies all homomorphisms to any finite group can be listed in finite time
2. Residually finite and all homomorphisms to any finite group can be listed in finite time implies solvable word problem

Proof

The proof follows directly by combining Facts (1) and (2).