File:Replacement1.png

This file was created as a diagram aid for Thompson's replacement theorem for abelian subgroups. It was created using Graphviz using the following code:

digraph G{
        rankdir="BT";
        A[label="A, abelian of maximum order"];
        B[label="B, abelian, normalized by but does not normalize A"];
        C[label="C = AB"];
        N[label="N = N_B(A)"];
        AcapB[label="Intersection of A and B"];
        P[label="P, whole group"];
        T[label="trivial subgroup"];
        T -> AcapB;
        AcapB -> N;
        AcapB -> A;
        N -> B[label="proper"];
        A -> C;
        B -> C;
        C -> P;
}