Let (G,∗) be a group. Prove that the right cancellation law holds in G. Provide reasons in your proof. (7.2) Write down all the subgroups of Z8. Why are they all cyclic? List all the generators of Z8. Explain why they are generators. Let G be a group, and let H and K be subgroups of G. Prove that H ∩K is a subgroup of G. For the group Z6, find two subgroups whose union is not a subgroup.

Let (G,∗) be a group. Prove that the right cancellation law holds in G. Provide reasons in your proof. (7.2) Write down all the subgroups of Z8. Why are they all cyclic? List all the generators of Z8. Explain why they are generators. Let G be a group, and let H and K be subgroups of G. Prove that H ∩K is a subgroup of G. For the group Z6, find two subgroups whose union is not a subgroup.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 12E

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