Abstract
The aim of this paper is to describe the B-injectors of the symmetric group S-n by proving the following main theorem, using a shorter proof than that followed in [1] and [3]. In this note the proof is mainly based on the minimal proof concept, and the parts we have used from these two papers are referred to.
Main Theorem: Let Omega be a finite set of size n, and let B <= S-Omega be a B-injector of S-Omega. Then
a) If n not equivalent to 3 (mod 4) then B is a Sylow 2-subgroup of S-Omega.
b) If n equivalent to 3 (mod 4) then B = < d > x T where d is a 3-cycle and T is a Sylow 2-subgroup of Cs-Omega (d).