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please do 7.2

please do 7.2

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.5: Isomorphisms
Problem 5E
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please do 7.2

QUESTION 7 (7.1) Let (G, *) be a group. Prove that the right cancellation law holds in G. Provide reaso asons. in your proof. (7.2) Write down all the subgroups of Zs. Why are they all cyclic? List all the generators of Zs. Explain why they are generators. (7.3) Let G be a group, and let H and K be subgroups of G. Prove that HK is a subgroup of G. (7.4) For the group Z6, find two subgroups whose union is not a subgroup.
Transcribed Image Text:QUESTION 7 (7.1) Let (G, *) be a group. Prove that the right cancellation law holds in G. Provide reaso asons. in your proof. (7.2) Write down all the subgroups of Zs. Why are they all cyclic? List all the generators of Zs. Explain why they are generators. (7.3) Let G be a group, and let H and K be subgroups of G. Prove that HK is a subgroup of G. (7.4) For the group Z6, find two subgroups whose union is not a subgroup.
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