Residual property (mathematics)
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(Redirected from Residually nilpotent)
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.
[edit] Examples
Important examples include:
- Residually finite
- Residually nilpotent
[edit] References
- Marshall Hall Jr (1959). The theory of groups. New York: Macmillan. p. 16.
