Answer 13 and 14 11. List12. Let G be a group and H be a finite non-empty subset of G that is closed underthe binary operation of G. Prove that H is a subgroup of G.13. Let : Z6→ Zs be the map defined as aAUTOCancelwhether is a homomorphism of groups.14. Compute the cyclic subgroup of R+ generated by .Compute the evclicsubgroupof Z generated by -1.O(a mod 5) for a € Z6. Determineft.Done

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Answered: the binary operation of 13. Let : Z6→…

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 32E: (See Exercise 31.) Suppose G is a group that is transitive on 1,2,...,n, and let ki be the subgroup...

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the binary operation of 13. Let : Z6→ Zs be the map defined as a (a mod 5) for a e Zo. Determine whether is a homomorphism of groups. 14, Compute the cyclic subgroup of R+ generated by .