6.55 (1978)

A group $G$ of the form $G = F \rtimes H$ is said to be a Frobenius group with kernel F and complement H if $H \cap H^g = 1$ for any $g \in G \setminus H$ and $F \setminus \{1\} = G \setminus \bigcup_{g \in G} H^g$. Do there exist Frobenius $p$-groups?