Solvability-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 solvability-forcing if it satisfies the following equivalent conditions:

• Every group of that order is solvable
• It has no non-prime divisor which is simple-feasible. In other words, no divisor of it occurs as the order of a simple non-Abelian group