# Number of nilpotent groups

1. Jun 5, 2012

### charlamov

characterize primes p and q for which each group of order pq is nilpotent

2. Jun 5, 2012

### DonAntonio

Hint: A finite group is nilpotent iff it is the direct product of its Sylow subgroups, so this leaves you almost without choice...

DonAntonio