# Omega subgroups are homomorph-containing

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Suppose $G$ is a group of prime power order (i.e., a finite $p$-group for some prime number $p$). Then, the omega subgroups of $G$, defined as:
$\Omega_j(G) := \langle x \mid x^{p^j} = e \rangle$
are homomorph-containing subgroups of $G$.