扶正器子范畴的欧拉示性数
Euler characteristics of centralizer subcategories
摘要：
设p是素数，G是有限群，A是作用在G上的有限群. G的非恒等p-子群的布朗偏序集则是A-偏序集。研究了G的等变子集和等变欧拉示性数，建立了局部定义的欧拉示性数与以A为中心的G的p元个数之间的整体关系.布朗定理的等变版本就是这个关系的一个推论：A-等变布朗偏序集的约化欧拉示性数可被A的中心化子的阶的p-部分整除。由于G在Brown偏序集上共轭的第二等变欧拉示性数与Knorr-Robinson猜想的关系，它是一个特别有趣的性质，我们在最小单Mathieu群的情形下对该猜想进行了具体的数值验证.
英文摘要：
Let p be a prime number, G a finite group, and A a finite group acting on G. The Brown poset of nonidentity p-subgroups of G is then an A-poset. We investigate the equivariant subposet and the equivariant Euler characteristics and establish a global relation between locally defined Euler characteristics and the number of p-elements of G centralized by A. It is a consequence of this relation that the equivariant version of Brown's theorem holds: The reduced Euler characteristic of the A-equivariant Brown poset is divisible by the p-part of the order of the centralizer of A. The second equivariant Euler characteristic for the conjugation of G on the Brown poset for G is especially intriguing because of its relation to the Knorr-Robinson conjecture and we carry out a concrete numerical verification of the conjecture in case of the smallest simple Mathieu group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
