Every group has a terminating transfinite automorphism tower
Proc. Amer. Math. Soc. 126 (1998), pp. 3223-3226 

Joel David Hamkins
Department of Mathematics, City University of New York, 
College of Staten Island, Staten Island, New York 10314 
URL: www.library.csi.cuny.edu/users/hamkins/ 

Abstract. Iteratively taking the automorphism group of any group leads, 
transfinitely, to a fixed point.