11. For a, b ∈ G, we have (ab)^-1=
A. ab
B. a^-1b^-1
C. b^-1a^-1
D. ba
12. The number of elements in a group is called its:
A. degree
B. order
C. power
D. None of these
13. The least positive integer n, such that a^n =… is called order of a.
A. e (identity)
B. a^-1
C. a
D. None of these
14. Let a ∈ G has order n. Then, for any integer k, a^k = e if and only if …, where q is an integer.
A. q = nk
B. n = qk
C. k = nq
D. None of these
15. If |a| = 5, then for what value of n, a
n = e?
A. 10
B. 15
C. 20
D. All of these
16. The set {1, 3, 5, 7} is a group under:
A. Addition
B. Multiplication
C. Addition modulo 8
D. Multiplication modulo 8
17. The set {1, 3, 5, 7} is a group under Multiplication modulo 8. The inverse of 5 is:
A. 1
B. 3
C. 5
D. 7
18. The set {1, 3, 5, 7} is a group under Multiplication modulo 8. The order of 5 is:
A. 1
B. 2
C. 3
D. 4
19. Let G be a group and a, b ∈ G, which of the following is true?
A. |a| = |a^-1|
B. |ab| = |ba|
C. |a| = |bab^-1|
D. All of these
20. Every group of … order contains at least one element of order 2.
A. Prime
B. Even
C. Odd
D. Composite
