MA8551 Important 8 Mark Questions ALGEBRA AND NUMBER THEORY
MA8551 Important 8 Mark Questions ALGEBRA AND NUMBER THEORY Regulation 2017 Anna University free download. ALGEBRA AND NUMBER THEORY Important 8 Mark Questions MA8551 pdf free download.
Sample MA8551 Important 8 Mark Questions ALGEBRA AND NUMBER THEORY
1.(a) Show that group homomorphism preserves identity, inverse, and sub group.
1. (b) Prove that, if (G,*) is a finite cyclic group generated by an element ???????????? and is of order n then ???????? = ???? so that ???? = {????, ????2, … ????????(= ????)} . Also n is the least positive integer for which ???????? = ????. MA8551 Important 8 Mark Questions Algebra And Number Theory
2. (a) Prove that the intersection of two subgroups of a group ???? is again a subgroup of ????
2.(b) Let ???? be a group and ???? ∈ ????. Let ????: ???? → ???? be given by
????(????) = ????????????−1, ∀ ???? ∈ ????. Prove that ???? is an isomorphism of
???? onto ????
3. (a) Show that ????2, the set of all 2????2 non singular matrices over ???? is a
group under usual matrix multiplication. Is it abelian? MA8551 Important 8 Mark Questions Algebra And Number Theory
3.(b) Show that the union of two subgroups of a group G is again a
subgroup of ???? if and only if one is contained in the other.
4. (a) State and prove Lagrange’s theorem MA8551 Important 8 Mark Questions Algebra And Number Theory
4.(b) In any ring (????, +, . ) (a) The zero element of ???? is unique (b) The
additive inverse of each element is unique
5. (a) Prove that the set ????4 = {0,1,2,3} is a commutative ring with respct
ot the binary operation +4 ???????????? ×4
7. (b) If G is a group of prime order, then G has no proper subgroups.
8. (a)
Prove that the necessary and sufficient condition for a non-empty
subset H of a group (????,∗)to be a subgroup is
????, ???? ∈ ???? ⇒ ???? ∗ ????−1 ∈ ????
| Subject name | ALGEBRA AND NUMBER THEORY |
| Short Name | ANT |
| Semester | 5 |
| Subject Code | MA8551 |
| Regulation | 2017 regulation |
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