Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.4: Cosets Of A Subgroup
Problem 11E: Let be a group of order 24. If is a subgroup of , what are all the possible orders of ?
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Please do the following questions with full handwritten working out.
![Question 3 Suppose G is a group, H is a subgroup, and a € G. Show |H| = |aH|. (Hint: build
a bijection from H to aH.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba18de34-fc06-47a6-b1ea-c54726b84874%2Fb3fd74f3-8f55-4c64-8493-6ee5afd12c5d%2F4drlxv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 3 Suppose G is a group, H is a subgroup, and a € G. Show |H| = |aH|. (Hint: build
a bijection from H to aH.)
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