Intermediately normal-to-complemented subgroup

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Definition

Symbol-free definition

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

• It is a complemented normal subgroup inside its normalizer.
• It is a lattice-complemented subgroup inside its normalizer.
• It is a permutably complemented subgroup inside its normalizer.
• It is a complemented normal subgroup inside any intermediate subgroup in which it is a normal subgroup.

Relation with other properties

Stronger properties

• Permuting transfer-closed normal-to-complemented subgroup