 Now let "P" act on Ω by conjugation.Let "Q" ∈ Ω0 and observe that then "Q" = "xQx"−1 for all "x" ∈ "P" so that "P" ≤ "NG"("Q").By Theorem 2, "P" and "Q" are conjugate in "NG"("Q") in particular, and "Q" is normal in "NG"("Q"), so then "P" = "Q".