Frobenius group

Summary

A Frobenius group is a finite transitive permutation group in which some non-identity element fixes a point, but no non-identity element fixes two points. The elements that fix no point, together with the identity, form a normal subgroup, the Frobenius kernel, by Frobenius's theorem. The group is then a semidirect product of the kernel and a point stabiliser, the Frobenius complement. Frobenius groups appear throughout finite group theory and character theory.