# Normal of order two implies central

From Groupprops

## Contents

## Statement

Suppose is a group and is a Normal subgroup (?) of that is of order two, i.e., it is isomorphic to Cyclic group:Z2 (?). Then, is a Central subgroup (?) of .

## Related facts

### Similar facts

- Normal of order equal to least prime divisor of group order implies central
- Cyclic normal Sylow subgroup for least prime divisor is central, which leads to cyclic Sylow subgroup for least prime divisor has normal complement
- Minimal normal implies central in nilpotent, minimal normal implies contained in Omega-1 of center for nilpotent p-group