Frobenius group
= Frobenius group
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A Frobenius group has a nontrivial proper subgroup $H$ satisfying $H\cap H^g=\{1\}$ for every $g\notin H$, with $H^g=g^{-1}Hg$. Such $H$ is a <Frobenius complement>. The <Frobenius kernel theorem> turns the identity together with elements outside all conjugates of $H$ into a normal subgroup $N$, giving $G=N\rtimes H$.