## The Center of a p-Group is Not Trivial

## Problem 10

Let $G$ be a group of order $|G|=p^n$ for some $n \in \N$.

(Such a group is called a $p$*-group*.)

Show that the center $Z(G)$ of the group $G$ is not trivial.

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Let $G$ be a group of order $|G|=p^n$ for some $n \in \N$.

(Such a group is called a $p$*-group*.)

Show that the center $Z(G)$ of the group $G$ is not trivial.

Add to solve later