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Ashot Minasyan
Ashot Minasyan
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A well-known theorem of Gruenberg implies that a finitely generated residually torsion-free nilpotent group is residually $p$-finite for all primes $p$. What about the converse?

Question: Are there any examples of a finitely generated group $G$ with the properties that $G$ is residually $p$-finite for all primes $p$, but $G$ is not residually torsion-free nilpotent?

A well-known theorem of Gruenberg implies that a residually torsion-free nilpotent group is residually $p$-finite for all primes $p$. What about the converse?

Question: Are there any examples of a group $G$ with the properties that $G$ is residually $p$-finite for all primes $p$, but $G$ is not residually torsion-free nilpotent?

A well-known theorem of Gruenberg implies that a finitely generated residually torsion-free nilpotent group is residually $p$-finite for all primes $p$. What about the converse?

Question: Are there any examples of a finitely generated group $G$ with the properties that $G$ is residually $p$-finite for all primes $p$, but $G$ is not residually torsion-free nilpotent?

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Ashot Minasyan
Ashot Minasyan
  • 3.2k
  • 21
  • 29

Residually nilpotent vs residually p

A well-known theorem of Gruenberg implies that a residually torsion-free nilpotent group is residually $p$-finite for all primes $p$. What about the converse?

Question: Are there any examples of a group $G$ with the properties that $G$ is residually $p$-finite for all primes $p$, but $G$ is not residually torsion-free nilpotent?