21. Let G be a group and the order of x ∈ G is odd. Then there exists an element y ∈ G
such that:
A. y = x
B. y2 = x
C. y = x2
D. y = x^3
23. Let G be a group and x2 = e, for all x ∈ G, then G is:
A. Abelian
B. Non Abelian
C. Commutative
D. Both A and C
25. Let G be a group. Which of the following is not unique in G?
A. identity
B. inverse of an element
C. idempotent
D. None of these
26. The set GL2(R) is the collection of all 2×2 matrices with real entries whose determinant
is:
A. Zero
B. Nonzero
C. Unit
D. 1
27. (Z, +) is a subgroup of:
A. (Z, +)
B. (R, +)
C. (C, +)
D. All of these
28. Every group has at least … subgroups.
A. 1
B. 2
C. 3
D. 4
29. A non empty subset of a group G is a subgroup of G if and only if for a, b ∈ H, we have:
A. ba−1 ∈ H
B. ab−1 ∈ H
C. ab ∈ H
D. Both A and B
30. The … of subgroups is a subgroup.
A. Intersection
B. Union
C. Difference
D. Symmetric difference
