On extensions of the Baer-Suzuki Theorem
- 72 Downloads
We find a necessary and sufficient condition for an element of prime order in a finite group to be in a normalp-subgroup. This generalizes the Baer-Suzuki Theorem. Our proof depends on a result about elements of prime order contained in a unique maximal subgroup containing a result of Wielandt. We discuss various consequences, linear and algebraic group versions of the result.
Unable to display preview. Download preview PDF.
- [A2]M. Aschbacher,Overgroups of Sylow subgroups in sporadic groups, Memoirs of the Amer. Math. Soc.60 (1986), No. 343.Google Scholar
- [H]J. Humphreys,Linear Algebric Groups, Springer-Verlag, New York, 1975.Google Scholar
- [St]R. Steinberg,Endomorphisms of linear algebraic groups, Mem. Amer. Math. Soc.,80, 1968.Google Scholar