# Full invariance is quotient-transitive

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., fully invariant subgroup) satisfying a subgroup metaproperty (i.e., quotient-transitive subgroup property)

View all subgroup metaproperty satisfactions | View all subgroup metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for subgroup properties

Get more facts about fully invariant subgroup |Get facts that use property satisfaction of fully invariant subgroup | Get facts that use property satisfaction of fully invariant subgroup|Get more facts about quotient-transitive subgroup property

## Contents

## Statement

### Statement with symbols

Suppose are groups, such that is a fully invariant subgroup of and is a fully invariant subgroup of . Then, is a fully invariant subgroup of .

## Related facts

### Generalization and other particular cases

A generalization of this fact is:

Other instances of this generalization are:

- Characteristicity is quotient-transitive
- Normality is quotient-transitive
- Strict characteristicity is quotient-transitive