. Which of the following groups are cyclic? (i) The group G of positive rational numbers which can be written as a/b with a and b odd, under multiplication. (ii) Z = {1, 2, 4, 5, 7, 8} under x modulo 9. (iii) The group H of matrices of the form (17), 01 with n Z, under matrix multiplication.
. Which of the following groups are cyclic? (i) The group G of positive rational numbers which can be written as a/b with a and b odd, under multiplication. (ii) Z = {1, 2, 4, 5, 7, 8} under x modulo 9. (iii) The group H of matrices of the form (17), 01 with n Z, under matrix multiplication.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.1: Definition Of A Group
Problem 38E: 38. Let be the set of all matrices in that have the form
with all three numbers , , and...
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Question
![3. Which of the following groups are cyclic?
(i) The group G of positive rational numbers which can be written as a/b with a and b odd,
under multiplication.
(ii) Z
{1, 2, 4, 5, 7, 8} under x modulo 9.
(iii) The group H of matrices of the form
=
1 n
01
1
with n Z, under matrix multiplication.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed029406-a1c1-473f-a3a0-6fd0fbd8e89d%2Ff4804512-08db-4d2f-a627-19d0f9aa7650%2Fu7b66ai5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Which of the following groups are cyclic?
(i) The group G of positive rational numbers which can be written as a/b with a and b odd,
under multiplication.
(ii) Z
{1, 2, 4, 5, 7, 8} under x modulo 9.
(iii) The group H of matrices of the form
=
1 n
01
1
with n Z, under matrix multiplication.
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