A proof of some conjecture about fixed points of automorphisms of $\mathbf{Z}_{p} \oplus \mathbf{Z}_{p^2}$

Daniel López-Aguayo

Published 2018-01-10Version 1

Let $G=\mathbf{Z}_{p} \oplus \mathbf{Z}_{p^2}$ where $p$ is a prime number. Suppose that $d$ is a divisor of $G$. In this paper we find the number of automorphisms of $G$ fixing $d$ elements of $G$, and denote it by $\theta(G,d)$. As a consequence, we prove Conjecture $1$ of [2].