Some Basic Properties Of The F_P（S₄）

Let G=S4, P is a Sylow-2-subgroup of S4, then we get a fusion system FP(G). In this paper, we propose the status of the study of fusion system,, recall some ba-sic definitions, theorems and properties of fusion system. We use FP(G) as an example get some of results such as fully F-centralised subgroups, fully F-normalised subgroups, the orbit category of F, normaliser, centraliser, K-normaliser, weakly F-closed group, strongly F-closed group, F-centric group, quotients of fusion systems, normal fusion systems, simple fusion systems, discuss some of basic properties of a fusion system, master some related theorems, inferences and basic conclusions. We obtained the concrete form of the conclusions of fusion system. We also use the conclusions of FP(G) as an example. The sixth section of chapter3verifies some main theorems about fusion systems from a computational paint of view.