# Self-centralizing and minimal normal implies fully invariant in co-Hopfian group

From Groupprops

## Statement

Suppose is a Co-Hopfian group (?) and is a Minimal normal subgroup (?) of that is also a Self-centralizing subgroup (?), i.e., . Then, is a Fully invariant subgroup (?) of .

## Facts used

- Self-centralizing and minimal normal implies monolith
- Monolith is fully invariant in co-Hopfian group

## Proof

The proof follows directly from facts (1) and (2).