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Santana Afton
Santana Afton
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This is an extension of a question I asked here on Math.SE

Assume that I have a finitely generated residually finite centerless group $G$. Is it true that the profinite completion $\hat{G}$ also has trivial center?

In the linked question, user YCor was able to show that this fails in general if you do not assume either finite generation or residually finite. However, the result is happens to be true if $G$ is a surface group. I’d like to know if this is a phenomenon specific to surface groups, or if this is a more general fact.

This is an extension of a question I asked here on Math.SE

Assume that I have a finitely generated residually finite centerless group $G$. Is it true that the profinite completion $\hat{G}$ also has trivial center?

In the linked question, user YCor was able to show that this fails in general if you do not assume either finite generation or residually finite. However, the result is happens to be true if $G$ is a surface group. I’d like to know if this is a phenomenon specific to surface groups or if this is a more general fact.

This is an extension of a question I asked here on Math.SE

Assume that I have a finitely generated residually finite centerless group $G$. Is it true that the profinite completion $\hat{G}$ also has trivial center?

In the linked question, user YCor was able to show that this fails in general if you do not assume either finite generation or residually finite. However, the result happens to be true if $G$ is a surface group. I’d like to know if this is a phenomenon specific to surface groups, or if this is a more general fact.

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YCor
YCor
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Santana Afton
Santana Afton
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Does a (nice) centerless group always have a centerless profinite completion?

This is an extension of a question I asked here on Math.SE

Assume that I have a finitely generated residually finite centerless group $G$. Is it true that the profinite completion $\hat{G}$ also has trivial center?

In the linked question, user YCor was able to show that this fails in general if you do not assume either finite generation or residually finite. However, the result is happens to be true if $G$ is a surface group. I’d like to know if this is a phenomenon specific to surface groups or if this is a more general fact.