File:Criticalsubgrouptheorem.png

A diagrammatic aid to the proof of Thompson's critical subgroup theorem. The file was created using Graphviz and the generating code is:

digraph G{       rankdir="BT"; K[label="K, maximal among abelian characteristic subgroups (CS1)"]; H[label="H = C_G(K), centralizer of K in G (CS3), characteristic in G (\ PS2)"]; G[label="G, whole group"]; L[label="L, inverse image of Omega_1(Z(G/K)) in G (CS6), characteristic\ in G (PS1)"]; C[label="C, intersection of H and L (CS7), characteristic in G (PS3), t\ he critical subgroup",peripheries=2]; K -> C[label="precisely center: PS5"]; C -> H;       C -> L;        K -> H[label="proper; see CS3"]; K -> L;       H -> G;        L -> G; }