Solvability-forcing number

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

Stronger properties

 * Weaker than::Odd number:
 * A number whose order has at most two distinct prime factors.
 * A number whose order is the product of three distinct primes.
 * Weaker than::Square-free number: A number whose order is a product of distinct primes.
 * Weaker than::Nilpotence-forcing number
 * Weaker than::Abelianness-forcing number
 * Weaker than::Cyclicity-forcing number