Nilpotency-forcing number

This article defines a property that can be evaluated for natural numbers

Definition

Symbol-free definition

A natural number is said to be nilpotence-forcing if the following equivalent conditions hold:

• Every group of that order is nilpotent
• Every group of that order is a direct product of its Sylow subgroups
• Every prime divisor of that number is Sylow-direct
• Every prime divisor of that number is Sylow-unique

Relation with other properties

Stronger properties

• Abelianness-forcing number
• Cyclicity-forcing number

Weaker properties

• Solvability-forcing number