A Survey of Some Questions and Results about Rank 3 Permutation Groups
نویسنده
چکیده
We use throughout the notation of [5], to which we refer for the basic theory of finite rank 3 permutation groups G. The solvable primitive rank 3 permutation groups have been determined by Foulser [4] and, independently, by Dornhoff [2]. Since rank 3 groups of odd order are solvable we assume that G has even order. Then the graphs JA and JT associated with the non-trivial orbitals A and T of G are a complementary pair of strongly regular graphs, both of which are connected if and only if G is primitive. We call a strongly regular graph primitive if it and its complement are connected. A rank 3 graph is defined to be a strongly regular graph whose automorphism group has rank 3 on the vertices.
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