Group in which every finite subgroup is nilpotent

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Definition

A group in which every finite subgroup is nilpotent is a group satisfying the property that every finite subgroup is a nilpotent group, and in particular, a finite nilpotent group.

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

Relation with other properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
p-group there is a prime number p such that the order of every element is a power of p. uses that prime power order implies nilpotent |FULL LIST, MORE INFO
group in which every finite subgroup is cyclic |FULL LIST, MORE INFO
group in which every finite subgroup is abelian |FULL LIST, MORE INFO
locally nilpotent group every finitely generated subgroup is nilpotent follows from finite implies finitely generated |FULL LIST, MORE INFO
group in which elements of coprime finite orders commute |FULL LIST, MORE INFO
group in which order of commutator divides order of element |FULL LIST, MORE INFO