Affiliation:
1. 1 King Abdulaziz University Department of Mathematics Jeddah Saudi Arabia
2. 2 Mu’tah University Department of Mathematics Mu’tah-Alkarak Jordan
Abstract
The aim of this paper is to describe the B-injectors of the symmetric group Sn 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 Ω be a finite set of size n, and let B ≦ SΩbe a B-injector of SΩ. Then
a)
If n ≢ 3 (mod 4) then B is a Sylow 2-subgroup of SΩ.
b)
If n ≡ 3 (mod 4) then B = 〈d〉 × T where d is a 3-cycle and T is a Sylow 2-subgroup of\documentclass{aastex}
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$C_{S_\Omega } (d)$
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