余类数理论与局部幂零p-群

设有限p-群G的阶是p^n,幂零类是c,则称r=n-c是G的余类数。局部幂零p-群的余类数是r当且仅当其每个有限子集都包含在一个余类数是r的有限p-子群里。目前余类数理论取得的主要成果在余类数是r的有限p-群和余类数为r的Pro-p-群上。本项目主要将利用余类数理论、特征标理论以及图论来研究余类数是r的局部幂零p-群的结构和性质，同时研究余类数是r的局部幂零p-群和余类数是r的有限p-群的特征标维数的性质。

Let G be a finite p-group of order p^n and nilpotent class c. Then r=n-c is called the coclass of G. A locally nilpotent p-group G has cocalss r if and only if each finite subset of G is contained in a finite subgroup of coclass r. Now the main results of the theory of coclass are in finite p-groups and Pro-p-groups. In this project, we will study the loaclly nilpotent p-groups of coclass of r by using the theory of cocalss, the theory of character and the theory of graph. Moreover, we will also study the property of the character degrees of locally nilpotent p-groups of coclass r and finite p-groups of coclass r.