profinite completion

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


where NfG means that N is a normal subgroupMathworldPlanetmath of finite index in G.

A group embeds into its profinite completion if and only if it is residually finite.

Title profinite completion
Canonical name ProfiniteCompletion
Date of creation 2013-03-22 15:15:54
Last modified on 2013-03-22 15:15:54
Owner yark (2760)
Last modified by yark (2760)
Numerical id 10
Author yark (2760)
Entry type Definition
Classification msc 20E18
Related topic AGroupsEmbedsIntoItsProfiniteCompletionIfAndOnlyIfItIsResiduallyFinite