OD-characterization And Non-commuting Graph Characterization Of Finite Almost Simple Groups

It is well known that finite(almost) simple groups are bricks of finite groups.In order to know better their properties and structures,it is very helpful for us to characterize them by their obvious,simple and instinctive properties.This paper is intended to study the following properties of finite almost simple groups:the degrees of vertices of their prime graphs and their non-communicating graphs.Obviously,there is an intimate relation between the former problem and a conjecture put forward by Professor Wujie Shi in 1987(see[53]).The latter one is related to another conjecture named AAM's conjecture put forward in J.Algebra in 2006(see[1]).Both of these conjectures are still unsolved completely.In Chapter 1,we introduce some symbols and basic concepts that we usually use in the paper.Moreover,we introduce some backgrounds and results of our research.In Chapter 2,we study OD-characterization of some finite almost simple groups. Namely,we classify some finite almost simple groups which have same orders and degrees of vertices of their prime graphs.Some results,partly or completely,generalize previous results technologically or extensively.In Chapter 3,we study characterization of some finite almost simple groups, specially those with connected prime graphs,by their non-communication graphs.Not only have we set up a link between AAM's conjecture and Thompson's conjecture for the finite simple groups with non-connected prime graphs,but also we have found a series of examples to show that the former conjecture is also true for the finite simple groups with connected prime graphs.At the end of the last two chapters,we leave a series of questions,which are unsolved.