Download OU B.Sc 2019 June-July 4th Semester 3121 Mathematics Question Paper

Note: Answer all questions.

= 60 Marks)

wer Type)

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om the questions. %

Let G be a group and e be an identity.

"'lf absHVa.beHand a"eHVaé

Sté!e and prove Lagrange theorem.

is either zero of prime.

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mom b"mth real coef?aents and let A denote

term O then prove that‘A is an ideal of R

gRtoaringSmenKerzp#l}eR/q; (n=0)

" 6 Let R[x] denotes |

subset of all po

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7 Let é be a ring homom

is an ideal of R.

8 IfDisan inWin then

9. (a) Every subgroup of a cyclic groug

• any subgroup of < a> is a divis

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• group < a > has exactly one subg

D[] is an integral domain.

clic more over if [< a[=n then the order of

n and for each positive divisor k of n, the :

of order K namely <a > .

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(b) »l‘)efrimr_e Altemayng group of Also prove that A, has order al ifn>1.

(a) Prove that the group of rotati ube is isomorphic to S.

(b) Let G be a group and let

abelian.

5 G .

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of G. If TG) is cyclic then G is - i

Code No. M2VE

(b)LetR be a commutative ring with

" integral domain if and only if A is e

R;,n>0monpr

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If R is a ring with unity and the ¢ facteristics of R is 0 then

g o contains angubn'ng lsom; p . I the charactoristic of

ring isomorphic (o & "N

a subring isomorp ” o}&

» b e : e

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(b)Let.s.s{(_"b a) / a.b»e. showthat ¢: €= n@

b(ar)= [_a[ a] s

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