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Post Reopened by Derek Holt, YCor, Jeremy Rickard, Stefan Kohl♦, Yemon Choi
reasked question with context
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YCor
YCor
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the relation between G' and Z(G) for a group G Perfect $p$-group with nontrivial center

For a $p$-group $G,$$G$, which we know has a nontrivial center, can we have $G=G'?$$G=G'$?

Obviously not when $G$ is finite. But the question makes sense for infinite groups (here $p$-group means that each element has finite order, which is a power of some given prime number $p$).

the relation between G' and Z(G) for a group G

For a $p$-group $G,$ which we know has a nontrivial center, can we have $G=G'?$

Perfect $p$-group with nontrivial center

For a $p$-group $G$, which we know has a nontrivial center, can we have $G=G'$?

Obviously not when $G$ is finite. But the question makes sense for infinite groups (here $p$-group means that each element has finite order, which is a power of some given prime number $p$).

Post Closed as "Not suitable for this site" by user6976, Emil Jeřábek, Alexey Ustinov, Chris Godsil, Leonid Positselski
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user122925
user122925
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the relation between G' and Z(G) for a group G

For a $p$-group $G,$ which we know has a nontrivial center, can we have $G=G'?$