Divisible normal subgroup

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This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): divisible group
View a complete list of such conjunctions
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

Definition

A subgroup of a group is termed a divisible normal subgroup if the subgroup is a divisible group and is also a normal subgroup of the whole group.

Relation with other properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
local divisibility-closed subgroup
divisibility-closed subgroup