Omega subgroups of a p-group

Definition

Let $p$ be a prime number and $P$ be a $p$-group. For any nonnegative integer $j$, the $j^{th}$ omega subgroup of $P$ is defined as:

${\mathrm{\Omega }}_j(P)=⟨x\in P\mid x^{p^j}=1⟩$.

See also

• Agemo subgroups of a p-group