本项目将研究几个涉及有限群的Sylow子群的问题，主要研究内容如下：.（1）试图解决Brauer第33问题：哪些2-群可以作为有限群G的Sylow 2-子群，使得G中对合构成一个共轭类。研究p阶子群皆共轭的有限群的p-可解性，研究非可解T-群（即对于任意素数p,自同构群传递地作用在所有p阶子群上的有限群）的结构。.（2）研究有限群的不可约特征标次数与其Sylow子群之间的关系。提出一个全新的猜想：设有限群G的p-块B的亏群为D，则|D:Z(D)|可由B中不可约特征标的最大高的某个函数所界定，这个猜想可以看作是著名的Brauer高零猜想必要性的推广，由这个猜想可导出Sylow p-子群的导长的一个上界。此外，试图通过特征标次数的恒等式与不等式来建立p-闭性的比较简单的判别准则。

In this project, we will study some problems related to the Sylow subgroups of finite groups. The main objects of this project are as follows:.(1) We will try to solve Brauer's problem 33：which 2-goup can be viewed as a Sylow 2-subgroup of a finite group G such that the involutions of G constitute a conjugacy class. We will also study the p-solvability of finite groups in which all subgroups of order p are conjugate and the structure of nonsolvable T-groups (for such group G, the automorphism group Aut(G) acts transitively on the subgroups of order p of G, where p is an arbitrary prime)..(2) We will explore the relationship between the degrees of irreducible characters of a finite group and its Sylow subgroups. We pose a new conjecture: Let D be the defect group of a p-block B of a finite group G, then |D:Z(D)| can be bounded by a function of the largest height of the irreducible characters in B. This conjecture can be viewed as a generalization of the necessity of the famous Brauer height zero conjecture，it can deduce an upper bound of the derived length of Sylow p-subgroup. Besides, we will establish some simpler criterion for p-closed group in terms of some identity or inequality of character degrees.