The Möbius function of \rm PSL(3,2^p) for any prime p

2019/03/31 by Martino Borello, Borello, Martino, Francesca Dalla Volta +3
Mathematics · Computer Science · #Finite Group Theory Research #Coding theory and cryptography #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1904.00471

Abstract

Let G be the simple group \rm PSL(3,2^p), where p is a prime number. For any subgroup H of G, we compute the Möbius function of H in the subgroup lattice of G. To this aim, we describe the intersections of maximal subgroups of G. We point out some connections of the Möbius function with other combinatorial objects, and, in this context, we compute the reduced Euler characteristic of the order complex of the subposet of r-subgroups of \rm PGL(3,q), for any prime r and any prime power q.

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