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; }