Frobenius kernel
= Frobenius kernel
{c}
{title2=$N=(G\setminus\bigcup_gH^g)\cup\{1\}$}
The Frobenius kernel consists of the identity and the elements lying in no conjugate of a <Frobenius complement>. The <Frobenius kernel theorem> proves that this conjugacy-invariant set is a <normal subgroup>, rather than assuming closure as part of its definition.