The M\"obius Function of the Affine Linear Group $\text{AGL}(1,\Bbb F_q)$

Abstract

Let $\text{AGL}(1,\Bbb F_q)$ denote the affine linear group of dimension one over the finite field $\Bbb F_q$. We determine the M\"obius function of the lattice of subgroups of $\text{AGL}(1,\Bbb F_q)$.