2015/02/04 by Jesper M. Møller, Møller, Jesper M.
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.1502.01317
32 pages; expanded with some changes in terminology
openalex publication_date 2015/02/04 · arxiv created 2015/04/21 · arxiv updated 2016/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.