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The power graph $\mathcal{G}(G)$ of a group $G$ is a simple graph whosevertices are the elements of $G$ and two distinct vertices are adjacent if oneis a power of other. In this paper, we investigate the Laplacian spectrum ofthe power graph $\mathcal{G}(\mathbb{Z}_{p^m}^n)$ of finite abelian $p$-group$\mathbb{Z}_{p^m}^n$. In particular, we prove that the spectrum of group$\mathbb{Z}_{p^m}^n$ is contained in the Laplacian spectrum of graph$\mathcal{G}(\mathbb{Z}_{p^m}^n)$. For a finite abelian group $G$ whose powergraph $\mathcal{G}(G)$ is planar, we also prove that the spectrum of group $G$is contained in the Laplacian spectrum of graph $\mathcal{G}(G)$.

The Laplacian spectrum of power graphs of some finite abelian p-groups