Baer–Suzuki theorem

In mathematical finite group theory, the Baer–Suzuki theorem, proved by (Baer 1957) and (Suzuki 1965), states that if any two elements of a conjugacy class C of a finite group generate a nilpotent subgroup, then all elements of the conjugacy class C are contained in a nilpotent subgroup. (Alperin Lyons) gave a short elementary proof.

References

• Alperin, J. L.; Lyons, Richard (1971), "On conjugacy classes of p-elements", Journal of Algebra 19: 536–537, doi:10.1016/0021-8693(71)90086-x, ISSN 0021-8693 
• Baer, Reinhold (1957), "Engelsche Elemente Noetherscher Gruppen", Mathematische Annalen 133: 256–270, doi:10.1007/BF02547953, ISSN 0025-5831 
• Gorenstein, D. (1980), Finite groups (2nd ed.), New York: Chelsea Publishing Co., ISBN 978-0-8284-0301-6, http://www.ams.org/bookstore-getitem/item=CHEL-301-H 
• Suzuki, Michio (1965), "Finite groups in which the centralizer of any element of order 2 is 2-closed", Annals of Mathematics, Second Series 82: 191–212, doi:10.2307/1970569, ISSN 0003-486X