Group in which every finite abelian subgroup is cyclic

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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

Definition

A group in which every finite abelian subgroup is cyclic is a group satisfying the following equivalent conditions:


Formalisms

In terms of the subgroup property collapse operator

This group property can be defined in terms of the collapse of two subgroup properties. In other words, a group satisfies this group property if and only if every subgroup of it satisfying the first property (finite abelian subgroup) satisfies the second property (finite cyclic subgroup), and vice versa.
View other group properties obtained in this way

Relation with other properties

Stronger properties