Divisible normal subgroup
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
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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 |