# Difference between revisions of "Finitely presented and conjugacy-separable implies solvable conjugacy problem"

From Groupprops

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* [[Finitely presented and residually finite implies solvable word problem]] | * [[Finitely presented and residually finite implies solvable word problem]] | ||

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+ | ==Facts used== | ||

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+ | # [[uses::Finitely presented implies all homomorphisms to any finite group can be listed in finite time]] | ||

+ | # [[uses::Conjugacy-separable and all homomorphisms to any finite group can be listed in finite time implies solvable conjugacy problem]] | ||

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+ | ==Proof== | ||

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

## Latest revision as of 00:04, 2 February 2012

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 conjugacy-separable group) must also satisfy the second group property (i.e., group with solvable conjugacy problem)

View all group property implications | View all group property non-implications

Get more facts about finitely presented conjugacy-separable group|Get more facts about group with solvable conjugacy problem

## Statement

A finitely presented conjugacy-separable group (i.e., a finitely presented group that is also a conjugacy-separable group) is a group with solvable conjugacy problem.

## Related facts

### Similar facts

## Facts used

- Finitely presented implies all homomorphisms to any finite group can be listed in finite time
- Conjugacy-separable and all homomorphisms to any finite group can be listed in finite time implies solvable conjugacy problem

## Proof

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