Group satisfying generalized subnormal join property

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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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Definition

A group is termed a group satisfying generalized subnormal join property if an arbitrary join of subnormal subgroups is also a subnormal subgroup.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Nilpotent group |FULL LIST, MORE INFO
Finite group FZ-group|FULL LIST, MORE INFO
Noetherian group every subgroup is finitely generated Group satisfying ascending chain condition on subnormal subgroups|FULL LIST, MORE INFO
Group satisfying ascending chain condition on subnormal subgroups |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Group satisfying subnormal join property a join of subnormal subgroups is subnormal |FULL LIST, MORE INFO