Residually nilpotent group
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This is a variation of nilpotence|Find other variations of nilpotence | Read a survey article on varying nilpotence
Definition
Symbol-free definition
A group is termed residually nilpotent if it satisfies the following equivalent conditions:
- Given any non-identity element, there is a normal subgroup not containing that element, such that the quotient group is nilpotent
- The lower central series reaches the identity element in countably many steps; in other words, the intersection of all the terms of the (finite) lower central series is the trivial group
Definition with symbols
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