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Groupprops β

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
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Contents

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