2005-9.md

course	course_year	question_number	tags	title	year
Groups, Rings and Modules	IB	9	IB 2005 Groups, Rings and Modules	2.II.11C	2005

Let $A$ be the abelian group generated by two elements $x, y$, subject to the relation $6 x+9 y=0$. Give a rigorous explanation of this statement by defining $A$ as an appropriate quotient of a free abelian group of rank 2. Prove that $A$ itself is not a free abelian group, and determine the exact structure of $A$.