NORMALIZERS OF P-SUBGROUPS IN FINITE GROUPS

In a recent paper, Sims obtained some striking applications of graph theory to group theory. Using his work, Wong determined every finite primitive permutation group in which the stabilizer of a point has some orbit of length three. The techniques of Sims and Wong can be applied to other situations that occur in investigations of finite groups. In this paper we obtain some applications that we will use in studying weakly closed elements of Sylow 2-subgroups. © 1969 by Pacific Journal of Mathematics.