Doubly Transitive Permutation Groups Which Are Not Doubly Primitive
نویسنده
چکیده
Hypothesis (A): G is a doubly transitive permutation group on a set Q. For 01 E Q, G, has a set Z = {B, , B, ,..., B,}, t > 2, which is a complete set of imprimitivity blocks on Q {a}. Let j Bi / = b > 1 for all i. Denote by H the kernel of G, on .Z and by Ki and K< the subgroups of G, fixing Bi setwise and pointwise respectively, 1 .< i < t. Let /3 E Bl . Here j Q j = 1 + ht. M. D. Atkinson has conjectured that a group satisfying (A) is either an automorphism group of a nontrivial block design with X = 1, or a normal extension of a Suzuki group, or must have a regular normal subgroup. We recall that the group Sx(q) satisfies (A) with H f 1, b = t = q and G,” is a-transitive. In the first part of this article we consider groups acting “like” a Suzuki group, namely:
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