Model Question Paper www.kannuruniversity.ac.in Kannur University : MSc Mathematics

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KANNUR UNIVERSITY
First Semester M.Sc. Degree Examinations
MATHEMATICS (2011 Syllabus)
MODEL QUESTION PAPER
MAT1C01: Algebra-I
Time: 3 Hours Maximum Weightage: 30

Model Question List : http://117.211.84.98/regulations/
Model Question Paper : http://117.211.84.98/regulations/modelmaths.pdf

Instructions: Answer any three questions from Part A. Each question in Part A has Weightage 2.
Answer any four questions from Part B. Each question in Part B has Weightage 3.
Answer any three questions from Part C without omitting any unit.
Each question in Part C has Weightage 4.

PART A
1. State the fundamental theorem of finitely generated abelian groups. Find all abelian groups, up to isomorphism, of order 1089

2. Define the normalizer of a subgroup of a group. Let G be a finite group and let p be a prime dividingG. Let P be a Sylow p-subgroup ofG. Show that [ []] [] N N P N P ? .

3. Define a free abelian group. Show that ? under addition is not a free abelian group.

4. Let F be a field and let () fx? [] Fxbe a non constant polynomial. When do you say that () fxis irreducible overF? Show that 4 2 2 8 1 x x x ? ? ? is irreducible over ?.

5. Define prime and maximal ideals of a ring. Prove that if Fis a field, every proper nontrivial prime ideal of [] Fxis a maximal ideal.

PART B
6. (a)If m divides the order of a finite abelian groupG, then show that G has a subgroup of order m.
(b)If G is indecomposable, show that G is cyclic with order a power of a prime.

7. State and prove the first isomorphism theorem.

8. Define a free abelian group. Let {0} G? be a free abelian group with a finite basis. Show that any two finite bases of G have the same number of elements.
(b) Find a polynomial of degree 0 ? in ????? that is a un

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http://117.211.84.98/regulations/modelmaec.pdf

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1-Advanced business accounting
2-Financial management
3-Taxation(Income tax)
4-Taxation2(Wealth tax &Indirect tax)
5-Budgeting and pricing
6-Financial markets and services
7-security analysis&Investment management
8-Business structure and practice
9-Corporate accounting