on the fusion of elementary abelian subgroups of a finite p-group

学生将研究融合系统对有限p群的非循环初等阿贝尔子群的偏序集的作用。动机来自这个偏序在描述有限群的内模群中的相关性，以及在群上同调中的初等阿贝尔p-子群的相关性（参见Benson， D. J.; Grodal， J.; Henke， E.，群上同调和p-融合的控制，Invent）。数学。农业学报，1997,491 -507,（2014）。学生将学习构成偏置熔断的p局部条件，主要是当熔断系统是由Sylow p-子群上的有限群定义时。人们期望孤立顶点的融合依赖于基本子群的存在，但仅凭这一信息可能还不够。

The student will investigate the action of fusion systems on the poset of noncyclic elementary abelian subgroups of a finite p-group. The motivation comes from the relevance of this poset in the description of the group of endotrivial modules of a finite group, and on the relevance of elementary abelian p-subgroups in group cohomology (cf. Benson, D. J.; Grodal, J.; Henke, E., Group cohomology and control of p-fusion, Invent. Math., 197, 491-507, (2014)). The student will study the p-local conditions that make components of the poset fuse, primarily when the fusion system is that defined by a finite group on a Sylow p-subgroup. One expects that the fusions of isolated vertices depend on the presence of essential subgroups, but this information alone may not suffice.