Question 1 |
Which of the following statements is/are TRUE for a group G?
MSQ
MSQ
If for all x,y \in G, (xy)^2=x^2y^2, then G is commutative. | |
If for all x \in G, x^2=1, then G is commutative. Here, 1 is the identity element of G. | |
If the order of G is 2 , then G is commutative. | |
If G is commutative, then a subgroup of G need not be commutative. |
Question 1 Explanation:
Question 2 |
Let G be a group of order 6, and H be a subgroup of G such that 1 < |H| < 6. Which one of the following options is correct?
Both G and H are always cyclic. | |
G may not be cyclic, but H is always cyclic. | |
G is always cyclic, but H may not be cyclic. | |
Both G and H may not be cyclic. |
Question 2 Explanation:
Question 3 |
Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is _______.
34 | |
35 | |
5 | |
7 |
Question 3 Explanation:
Question 4 |
(G,*) is an abelian group. Then
x=x^{-1} for any x belonging to G | |
x=x^{2} for any x belonging to G | |
(x * y)^{2}=x^{2} * y^{2} , for any x,y belonging to G | |
G is of finite order |
Question 4 Explanation:
Question 5 |
Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is ________.
42 | |
21 | |
24 | |
84 |
Question 5 Explanation:
There are 5 questions to complete.
Please add a feature to BOOKMARK questions for revision. It would be really helpful.
check question 20 ,answer should be option c
For the Q24, The answer is option C