Complemented transitively normal subgroup

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: permutably complemented subgroup and transitively normal subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

Symbol-free definition

A subgroup of a group is termed a complemented transitively normal subgroup if it satisfies the following equivalent conditions:

• It is a permutably complemented subgroup as well as a transitively normal subgroup.
• It is a complemented normal subgroup as well as a transitively normal subgroup.

Relation with other properties

Stronger properties

• Direct factor
• Complemented central factor

Weaker properties

• Complemented normal subgroup
• Transitively normal subgroup
• Normal subgroup