Normal subgroup having a 1-closed transversal
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: normal subgroup and subgroup having a 1-closed transversal
View other subgroup property conjunctions | view all subgroup properties
Definition
A normal subgroup having a 1-closed transversal is a normal subgroup that is also a subgroup having a 1-closed transversal: it has a left transversal that is also a 1-closed subset of the group (i.e., a union of subgroups of the group).
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Complemented normal subgroup | normal, has a permutable complement | |FULL LIST, MORE INFO | ||
| Direct factor | normal, has a normal complement | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Subgroup having a 1-closed transversal | ||||
| Normal subgroup | ||||
| Subgroup having a left transversal that is also a right transversal | |FULL LIST, MORE INFO |