2017-31.md

course	course_year	question_number	tags	title	year
Groups, Rings and Modules	IB	31	IB 2017 Groups, Rings and Modules	Paper 4, Section I, $2 E$	2017

Let $G$ be a non-trivial finite $p$-group and let $Z(G)$ be its centre. Show that $|Z(G)|>1$. Show that if $|G|=p^{3}$ and if $G$ is not abelian, then $|Z(G)|=p$.