Group satisfying generalized subnormal join property

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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				|FULL LIST, MORE INFO
Noetherian group	every subgroup is finitely generated			|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