Complemented fully invariant subgroup

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

Definition

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

1. It is both a permutably complemented subgroup and a fully invariant subgroup.
2. It is both a lattice-complemented subgroup and a fully invariant subgroup.
3. It is both a complemented normal subgroup and a fully invariant subgroup.

Relation with other properties

Stronger properties

• Normal Sylow subgroup
• Normal Hall subgroup
• Fully invariant direct factor
• Complemented homomorph-containing subgroup

Weaker properties

• Fully invariant subgroup
  • Characteristic subgroup
  • Normal subgroup
• Complemented characteristic subgroup
• Complemented normal subgroup