2015-34.md

course	course_year	question_number	tags	title	year
Groups, Rings and Modules	IB	34	IB 2015 Groups, Rings and Modules	Paper 3, Section II, F	2015

Can a group of order 55 have 20 elements of order 11? If so, give an example. If not, give a proof, including the proof of any statements you need.

Let $G$ be a group of order $p q$, with $p$ and $q$ primes, $p>q$. Suppose furthermore that $q$ does not divide $p-1$. Show that $G$ is cyclic.