This article defines a property that can be evaluated for natural numbers
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
A natural number is said to be nilpotency-forcing or nilpotence-forcing if the following equivalent conditions hold:
- Every group of order is nilpotent
- Every group of order is a direct product of its Sylow subgroups
- Every prime divisor of is Sylow-direct
- Every prime divisor of is Sylow-unique
- Suppose are prime divisors of and is the largest power of dividing . Then, the order of modulo exceeds . In other words, does not divide for .
For proof of the equivalence of definitions, see classification of nilpotency-forcing numbers.