# Divisibility condition on Sylow numbers

From Groupprops

*This article gives the statement, and possibly proof, of a constraint on numerical invariants that can be associated with a finite group*

This article states a result of the form that one natural number divides another. Specifically, the (number) of a/an/the (Sylow subgroup) divides the (index) of a/an/the (Sylow subgroup).

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## Statement

Suppose is a finite group of order:

where is prime, is a nonnegative integer, and is relatively prime to . Let denote the -Sylow number (?), i.e., the number of -Sylow subgroups of . Then we have:

.