Nilpotent Groups of Finite Morley Rank
نویسندگان
چکیده
Now assume |G : H| is infinite and that H is definable in G (but H need no longer be infinite or G-normal). Let Z = Z◦(G), and note that (a) implies that Z is infinite. If |Z : H ∩Z| is infinite, then |HZ : H| is infinite as well. In this case we are done since H ≤ HZ ≤ NG(H). Otherwise, |Z : H ∩Z| is finite, so the connectedness of Z implies that Z ≤ H. We can now proceed by induction on the rank of G to get that |NG/Z(H/Z) : H/Z| is infinite. Now NG/Z(H/Z)/(H/Z) = (NG(H)/Z)/(H/Z) ∼= NG(H)/H.
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