Group in which every cyclic subgroup is 2-subnormal

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Definition

Symbol-free definition

A group in which every cyclic subgroup is 2-subnormal is a group with the property that every cyclic subgroup (i.e., the subgroup generated by any subset of the group) of the group is a 2-subnormal subgroup.

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 (cyclic subgroup) satisfies the second property (cyclic 2-subnormal subgroup), and vice versa.
View other group properties obtained in this way

Relation with other properties

Stronger properties

Weaker properties