Frobenius group

A permutation groupMathworldPlanetmath G on a set X is Frobenius if no non-trivial element of G fixes more than one element of X. Generally, one also makes the restrictionPlanetmathPlanetmathPlanetmath that at least one non-trivial element fix a point. In this case the Frobenius group is called non-regular.

The stabilizerMathworldPlanetmath of any point in X is called a Frobenius complement, and has the remarkable property that it is distinct from any conjugate by an element not in the subgroupMathworldPlanetmathPlanetmath. Conversely, if any finite groupMathworldPlanetmath G has such a subgroup, then the action on cosets of that subgroup makes G into a Frobenius group.

Title Frobenius group
Canonical name FrobeniusGroup
Date of creation 2013-03-22 13:16:30
Last modified on 2013-03-22 13:16:30
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 5
Author bwebste (988)
Entry type Definition
Classification msc 20B99
Defines Frobenius complement