2019-33.md

course	course_year	question_number	tags	title	year
Groups, Rings and Modules	IB	33	IB 2019 Groups, Rings and Modules	Paper 4, Section II, G	2019

(a) Define the Smith Normal Form of a matrix. When is it guaranteed to exist?

(b) Deduce the classification of finitely generated abelian groups.

(c) How many conjugacy classes of matrices are there in $G L_{10}(\mathbb{Q})$ with minimal polynomial $X^{7}-4 X^{3} ?$