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The answer is "no". The lamplighter group (which is infinitely presented) is a limit of a sequence of virtually free groups and surjective homomorphisms (see, for example, this question and answers there). All virtually free groups are residually finite.

The answer is "no". The lamplighter group (which is infinitely presented) is a limit of a sequence of virtually free groups and surjective homomorphisms (see, for example, this question and answers there. All virtually free groups are residually finite.

The answer is "no". The lamplighter group (which is infinitely presented) is a limit of a sequence of virtually free groups and surjective homomorphisms (see, for example, this question and answers there). All virtually free groups are residually finite.

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markvs
  • 1.8k
  • 1
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  • 25

The answer is "no". The lamplighter group (which is infinitely presented) is a limit of a sequence of virtually free groups and surjective homomorphisms (see, for example, this question and answers there. All virtually free groups are residually finite.