2013-30.md

course	course_year	question_number	tags	title	year
Groups, Rings and Modules	IB	30	IB 2013 Groups, Rings and Modules	Paper 4, Section I, $2 G$	2013

Let $p$ be a prime number, and $G$ be a non-trivial finite group whose order is a power of $p$. Show that the size of every conjugacy class in $G$ is a power of $p$. Deduce that the centre $Z$ of $G$ has order at least $p$.