245544

D 30568 (Pages : 3) ಸ ಭಾ ಕ್ಷ ಿುುಿು್ತ

FIFTH SEMESTER (CBCSS-UG) DEGREE EXAMINATION
NOVEMBER 2022

Mathematics
MTS 5B 05—ABSTRACT ALGEBRA
(2020 Admission onwards)
Time : Two Hours and a Half Maximum : 80 Marks
Section A

Answer any number of questions.
Each question carries 2 marks.
Ceiling is 25.

1. Write addition and multiplication tables for Z,.

2. Check whether the relation on defined by a ~ 6 if n| (a — b), where n is a positive integer is an
equivalence relation.

3. Consider the following permutations in S, :

123 4567 12\3 45 67
तिर and t=
6 25461 7 (4 1 5 7 4 6 ॥।

Compute ot and to.
4. Show that cancellation property holds in a group G.

5. Find all cyclic subgroups of the group ‏.أ2‎

-1 1
6. Find the order of the element | 0 1 in GL, (R).

7. Give addition table for Z, x Zo.
8. Show that composite of two group isomorphisms is a group isomorphism.

9. Give the subgroup diagrams of Z.,.

Turn over

245544