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The affine permutation groups of rank three. (English) Zbl 0621.20001
The object of the present paper is to complete the classification of finite primitive permutation groups G of rank 3 by treating the case that G is an affine group, acting on a vector space V of dimension d over GF(p).
The other cases have been treated successfully by Bannai, Cameron, Kantor and Liebler, Liebeck and Saxl in various research papers. The proof uses the classification of finite simple groups. It should be noticed that the methods used in the paper are also suitable for obtaining the results of C. Hering on 2-transitive affine groups [J. Algebra 93, 151-164 (1985; Zbl 0583.20003)].
Reviewer: W.Knapp

MSC:
20B15 Primitive groups
20B10 Characterization theorems for permutation groups
20D06 Simple groups: alternating groups and groups of Lie type
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