Cyclic implies every subgroup is characteristic

Statement

In a cyclic group, every subgroup is a characteristic subgroup.

Related facts

Stronger facts

• Cyclic implies every subgroup is quotient-isomorph-free
• Cyclic implies every subgroup is verbal
• Finite cyclic implies every subgroup is isomorph-free
• Locally cyclic and periodic implies every subgroup is characteristic

Converse

• Finite and every subgroup is characteristic implies cyclic