Normal subgroup having a 1-closed transversal

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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 Complemented normal subgroup|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