# profinite completion

The profinite completion of a group $G$ is defined to be the profinite group

 $\hat{G}=\varprojlim_{N\trianglelefteqslant_{\mathrm{f}}G}G/N,$

where $N\trianglelefteqslant_{\mathrm{f}}G$ means that $N$ is a normal subgroup of finite index in $G$.

Title profinite completion ProfiniteCompletion 2013-03-22 15:15:54 2013-03-22 15:15:54 yark (2760) yark (2760) 10 yark (2760) Definition msc 20E18 AGroupsEmbedsIntoItsProfiniteCompletionIfAndOnlyIfItIsResiduallyFinite