we know that if $G$ is a finite $p$-group whit $|G|\gt1$. then $Z(G)$,the center of $G$, has more than one element.for proof of this we use the $|G|=|Z(G)|+\sum[G:C(a)]$ st $a\notin Z(G)$. is the way show $Z(G)\gt1$ whit out use class equation?


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