Pi-group ($\pi \text{-group}$)

For a set $\pi$ of primes, a pi-group is a finite group whose order has no prime divisors outside $\pi$. The trivial group qualifies for every $\pi$.

A pi-element is an element whose order has no prime divisors outside a specified prime set $\pi$. The identity is a pi-element for every prime set. Conjugation preserves the property because it preserves element order.