Carmichael numbers for $\mathrm{GL}(m)$

Abstract

We propose a generalization of Carmichael numbers, where the multiplicative group ${\mathbb{G}}_{\mathrm{m}}=\mathrm{GL}(1)$ is replaced by $\mathrm{GL}(m)$ for $m\ge 2$. We prove basic properties of these families of numbers and give some examples.

10 pages