Residual property (mathematics)
- Residual property (mathematics)
In the mathematical field of group theory, a group is residually "X" (where "X" is some property of groups) if it "can be recovered from groups with property "X".
Formally, a group "G" is residually "X" if for every non-trivial element "g" there is a homomorphism "h" from "G" to a group with property "X" such that .
More categorically, a group is residually "X" if it embeds into its pro-"X" completion (see profinite group, pro-p group), that is, the inverse limit of where "H" is a group with property "X".
Examples
Important examples include:
* Residually finite
* Residually nilpotent
References
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