Questions tagged [frobenius-groups]

Use this tag for questions about Frobenius groups, kernels and complements.

A Frobenius group is a transitive permutation group on a finite set, such that no non-trivial element fixes more than one point and some non-trivial element fixes a point. Alternatively, G is a Frobenius group if and only if G has a proper, nonidentity subgroup H such that H ∩ Hg is the identity subgroup for every g ∈ G − H, i.e. H is a malnormal subgroup of G.

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Order Frobenius complement divides order Frobenius kernel - 1

Let $G$ be a Frobenius group with $H$ Frobenius complement and $K$ Frobenius kernel. I read that $|H|$ divides $|K| - 1$, but I don't know why this holds, has anyone an idea?