6.53 (1978)
SolvedA 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 $F \setminus \{1\} = G \setminus \bigcup_{g \in G} H^g$. What can be said about the kernel and the complement of a Frobenius group? In particular, which groups can be kernels? complements?
Progress
Every group can be embedded into the kernel of a Frobenius group, and every right-orderable group can be a complement in a Frobenius group (V. V. Bludov, Siberian Math. J., 38, no. 6 (1997), 1054–1056).
Proof claims
Proof claims are the responsibility of the submitter. Appearance here does not mean the claim has been checked for mathematical correctness.
Moderators only screen for spam, abuse, and obviously low-effort submissions.
No proof claims yet.
Log in to claim a proof.
Comments
No comments yet. Be the first to comment.
Log in to post a comment.