Frobenius group
A permutation group
on a set is Frobenius if no non-trivial element of fixes more than
one element of . Generally, one also makes the restriction
that at least one non-trivial element
fix a point. In this case the Frobenius group is called non-regular.
The stabilizer of any point in is called a Frobenius complement, and has the remarkable
property that it is distinct from any conjugate by an element not in the subgroup
. Conversely,
if any finite group
has such a subgroup, then the action on cosets of that subgroup makes
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 |