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Frobenius Kernel

Need:
1
 Time:
2
Component: Permutation
Contact: GAP group
( support@gap-system.org)
Last Update: 1999/2/19
Math:
4
 Program:
-

Description

The Frobenius Kernel $K=\{x\in G\mid fix(x)=\emptyset\}\cup\{1\}$ is a nilpotent normal subgroup in a frobenius group. How could it be computed? (One could check all normal subgroups in F(G) but there might be a better way\ .)

Usage

\> FrobeniusKernel(<G>)

If <G> is a Frobenius group this operation returns the frobenius kernel,\ that is the nilpotent normal subgroup $K=\{x\in G\mid fix(x)=\emptyset\}\cup\{1\}$. (What happens if <G> is not Frobenius?) 

\beginexample
gap> frob:=TransitiveGroup(5,3);
F(5) = 5:4
gap> FrobeniusKernel(frob);
Group([ (1,2,3,4,5) ])
\endexample

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