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Primitive Permutation Groups of Prime Power Degree

Brian Mortimer

出版	University of Alberta, 1975
URL	http://books.google.com.hk/books?id=ztTY0AEACAAJ&hl=&source=gbs_api

註釋

In 1969, H. Wielandt [12] developed a new method for studying permutation groups by using the algebra of functions mapping the permuted set into a field. Using this technique he was able to classify the 2 uni-primitive groups of degree p In this thesis we apply the Wielandt method to the case of 3 degree p.Chapter III is devoted to generalizing these techniques to more than two variables and to general results on primitivity. Chapter IV contains the main theorems. It is shown there (Theorem 4.1) 3 that a uni-primitive group of degree p containing a regular elementary abelian subgroup is either contained in the affine group, "almost" imprimitive or else very non-geometric. Finally, the last two possibilities are eliminated when p = 3 (Theorem 4.6).