# Omega subgroups are homomorph-containing

From Groupprops

This article gives the statement, and possibly proof, of the fact that for any group, the subgroup obtained by applying a given subgroup-defining function (i.e., omega subgroups of group of prime power order) always satisfies a particular subgroup property (i.e., homomorph-containing subgroup)}

View subgroup property satisfactions for subgroup-defining functions View subgroup property dissatisfactions for subgroup-defining functions

## Statement

Suppose is a group of prime power order (i.e., a finite -group for some prime number ). Then, the omega subgroups of , defined as:

are homomorph-containing subgroups of .