Page 129 - DMTH403_ABSTRACT_ALGEBRA

Abstract Algebra

Notes 10.6 Review Questions

1. Compute all possible finite abelian groups of order n. What is the largest n for which it
will work?
2. Find all finite abelian group of order less than or equal to 40 up to isomorphism.
3. Find all finite abelian groups of order 200 to 720 up to isomorphism.

4. Show that the infinite direct product G = Z × Z × . . . is not finitely generated.
2
2
5. Let G be a finite abelian group of order m. If n divides m, prove that G has a subgroup of
order n.
Answers: Self Assessment

1. (c) 2. (a) 3. (a) 4. (a) 5. (c)

10.7 Further Readings

Books Dan Saracino: Abstract Algebra; A First Course.
Mitchell and Mitchell: An Introduction to Abstract Algebra.
John B. Fraleigh: An Introduction to Abstract Algebra (Relevant Portion).

Online links www.jmilne.org/math/CourseNotes/
www.math.niu.edu
www.maths.tcd.ie/
archives.math.utk.edu

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